{"segment":[{"time":24,"part":[{"title":"\u0110i\u1ec1n d\u1ea5u v\u00e0 s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[[">"],["7"]]],"list":[{"point":5,"width":50,"content":"","type_input":"","ques":"Gi\u1ea3i b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh: $6x - 13 > 4x + 1$<br\/><b>\u0110\u00e1p \u00e1n:<\/b> $x$ _input_ _input_","hint":"","explain":"<span class='basic_left'>Ta c\u00f3:<br\/>$6x - 13 > 4x + 1$ <br\/> $\\Leftrightarrow 6x - 4x > 1 + 13$ <br\/>$\\Leftrightarrow 2x > 14 $<br\/>$\\Leftrightarrow x > 14 : 2 $<br\/>$\\Leftrightarrow x > 7 $<br\/>V\u1eady t\u1eadp nghi\u1ec7m c\u1ee7a b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 $\\left\\{x \\mid x > 7\\right\\}$<br\/>D\u1ea5u v\u00e0 s\u1ed1 c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u1ea7n l\u01b0\u1ee3t l\u00e0 <span class='basic_pink'>\">\"; $7$<\/span><\/span>"}]}],"id_ques":1221},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai28/lv2/img\/3.jpg' \/><\/center><br\/>Gi\u1ea3i b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh $6x - 16 < -4x + 34$","select":[" A. $\\left\\{x \\mid x > 5\\right\\}$"," B. $\\left\\{x \\mid x < 5\\right\\}$","C. $\\left\\{x \\mid x > 9 \\right\\}$","D. $\\left\\{x \\mid x < 9 \\right\\}$"],"hint":"S\u1eed d\u1ee5ng quy t\u1eafc chuy\u1ec3n v\u1ebf v\u00e0 quy t\u1eafc nh\u00e2n ho\u1eb7c quy t\u1eafc chia v\u1edbi m\u1ed9t s\u1ed1 \u0111\u1ec3 gi\u1ea3i.","explain":"<span class='basic_left'>Ta c\u00f3 $6x - 16 < -4x + 34$<br\/>$\\Leftrightarrow 6x + 4x < 34 + 16$<br\/>$\\Leftrightarrow 10x < 50$<br\/>$\\Leftrightarrow x < 50 : 10$ <br\/>$\\Leftrightarrow x < 5$<br\/>V\u1eady t\u1eadp nghi\u1ec7m c\u1ee7a b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 $\\left\\{x \\mid x < 5\\right\\}$ <br\/>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'>B. $\\left\\{x \\mid x < 5\\right\\}$<\/span><\/span>","column":2}]}],"id_ques":1222},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai28/lv2/img\/5.jpg' \/><\/center> T\u00ecm c\u00e1c nghi\u1ec7m nguy\u00ean d\u01b0\u01a1ng c\u1ee7a b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh: $18 - 3x \\geq 0$<\/span>","select":[" A. $x \\in \\left\\{1; 2; 3; 4; 5\\right\\}$"," B. $x \\in \\left\\{ 2; 3; 4; 5; 6\\right\\}$","C. $x \\in \\left\\{1; 2; 3; 4; 5; 6\\right\\}$","D. $x \\in \\left\\{0; 1; 2; 3; 4; 5\\right\\}$"],"hint":"S\u1eed d\u1ee5ng quy t\u1eafc chuy\u1ec3n v\u1ebf v\u00e0 quy t\u1eafc nh\u00e2n v\u1edbi m\u1ed9t s\u1ed1 \u0111\u1ec3 gi\u1ea3i b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh t\u1eeb \u0111\u00f3 t\u00ecm ra k\u1ebft qu\u1ea3 c\u1ea7n t\u00ecm.","explain":"<span class='basic_left'>Ta c\u00f3 $18 - 3x \\geq 0$<br\/>$\\Leftrightarrow 3x \\leq 18$<br\/>$\\Leftrightarrow x \\leq 18 : 3$<br\/>$\\Leftrightarrow x \\leq 6$<br\/>V\u1eady c\u00e1c nghi\u1ec7m nguy\u00ean d\u01b0\u01a1ng c\u1ee7a b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 $x \\in \\left\\{1; 2; 3; 4; 5; 6\\right\\}$ <br\/>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'>C.$x \\in \\left\\{1; 2; 3; 4; 5; 6\\right\\}$<\/span><\/span>","column":2}]}],"id_ques":1223},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai28/lv2/img\/6.jpg' \/><\/center> T\u00ecm c\u00e1c nghi\u1ec7m nguy\u00ean \u00e2m c\u1ee7a b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh: $5x + 12 \\geq -3$<\/span>","select":[" A. $x \\in \\left\\{-2; -1\\right\\}$"," B. $x \\in \\left\\{ -3; -2; -1\\right\\}$","C. $x \\in \\left\\{-3; -2; -1; 0\\right\\}$","D. $x \\in \\left\\{-4; -3; -2; -1\\right\\}$"],"hint":"S\u1eed d\u1ee5ng quy t\u1eafc chuy\u1ec3n v\u1ebf v\u00e0 quy t\u1eafc nh\u00e2n v\u1edbi m\u1ed9t s\u1ed1 \u0111\u1ec3 gi\u1ea3i b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh t\u1eeb \u0111\u00f3 t\u00ecm ra k\u1ebft qu\u1ea3 c\u1ea7n t\u00ecm.","explain":"<span class='basic_left'>Ta c\u00f3 $5x + 12 \\geq -3$<br\/>$\\Leftrightarrow 5x \\geq -3 - 12$<br\/>$\\Leftrightarrow 5x \\geq -15$<br\/>$\\Leftrightarrow x \\geq -15 : 5$<br\/>$\\Leftrightarrow x \\geq -3$<br\/>V\u1eady c\u00e1c nghi\u1ec7m nguy\u00ean \u00e2m c\u1ee7a b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 $x \\in \\left\\{-3; -2; -1\\right\\}$ <br\/>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'>B.$x \\in \\left\\{-3; -2; -1\\right\\}$<\/span><\/span>","column":2}]}],"id_ques":1224},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai28/lv2/img\/5.jpg' \/><\/center> Trong c\u00e1c b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh b\u1eadc nh\u1ea5t m\u1ed9t \u1ea9n sau \u0111\u00e2y, $x = 6$ l\u00e0 nghi\u1ec7m c\u1ee7a b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh n\u00e0o ?<\/span>","select":[" A. $2x + 5 > 16$"," B. $x - 7 < 2x - 13$","C. $x + 5 > 2x - 1$","D. $-x + 8 < x - 9$"],"hint":"Thay $x = 6$ v\u00e0o t\u1eebng b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh \u0111\u1ec3 ki\u1ec3m tra.","explain":"<span class='basic_left'>Ta c\u00f3:<br\/>+ Thay $x = 6$ v\u00e0o b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh $2x + 5 > 16$ ta \u0111\u01b0\u1ee3c:<br\/>$2.6 + 5 > 16 \\Leftrightarrow 17 > 16$ (lu\u00f4n \u0111\u00fang)<br\/>$\\Rightarrow x = 6$ l\u00e0 nghi\u1ec7m c\u1ee7a b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh $2x + 5 > 16$<br\/>+ Thay $x = 6$ v\u00e0o b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh $x - 7 < 2x - 13$, ta \u0111\u01b0\u1ee3c:<br\/>$6 - 7 < 2.6 - 13 \\Leftrightarrow -1 < -1$ (v\u00f4 l\u00ed)<br\/>$\\Rightarrow x = 6$ kh\u00f4ng l\u00e0 nghi\u1ec7m c\u1ee7a b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh $x - 7 < 2x - 13$<br\/>+ Thay $x = 6$ v\u00e0o b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh $x + 5 > 2x - 1$, ta \u0111\u01b0\u1ee3c:<br\/>$6 + 5 > 2.6 - 1 \\Leftrightarrow 11 > 11$ (v\u00f4 l\u00fd)<br\/>$\\Rightarrow x = 6$ kh\u00f4ng l\u00e0 nghi\u1ec7m c\u1ee7a b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh $x + 5 > 2x - 1$<br\/>+ Thay $x = 6$ v\u00e0o b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh $-x + 8 < x - 9$ ta \u0111\u01b0\u1ee3c:<br\/> $-6 + 8 < 6 - 9 \\Leftrightarrow 2 < -3$ (v\u00f4 l\u00fd)<br\/>$\\Rightarrow x = 6$ kh\u00f4ng l\u00e0 nghi\u1ec7m c\u1ee7a b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh $-x + 8 < x - 9$<br\/>V\u1eady ta ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'>A. $2x + 5 > 16$<\/span> <\/span><br\/><span class='basic_left'><span class='basic_green'>Nh\u1eadn x\u00e9t:<\/span><br\/> Ngo\u00e0i c\u00e1ch l\u00e0m tr\u00ean ta c\u00f3 th\u1ec3 th\u1ef1c hi\u1ec7n gi\u1ea3i t\u1eebng b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh, t\u1eeb \u0111\u00f3 t\u00ecm ra \u0111\u00e1p \u00e1n c\u1ea7n t\u00ecm<\/span> <br\/><br\/>","column":2}]}],"id_ques":1225},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai28/lv2/img\/5.jpg' \/><\/center> B\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh $x^2 - 6x + 12 > 0$ nghi\u1ec7m \u0111\u00fang v\u1edbi m\u1ecdi $x$. <b>\u0110\u00fang<\/b> hay <b> Sai<\/b>?<\/span>","select":[" A. \u0110\u00fang"," B. Sai"],"hint":"","explain":"<span class='basic_left'><span class='basic_green'>Ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i:<\/span><br\/>Bi\u1ebfn \u0111\u1ed5i b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh v\u1ec1 d\u1ea1ng $\\left[f(x)\\right]^2 + k > 0$ (v\u1edbi $k > 0$)<\/span> <br\/><span class='basic_left'><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Ta c\u00f3: $x^2 - 6x + 12 = (x^2 - 6x + 9) + 3 = (x - 3)^2 + 3$<br\/>V\u00ec $(x - 3)^2 \\geq 0$ v\u1edbi m\u1ecdi $x$ n\u00ean $(x - 3)^2 + 3 > 0$ v\u1edbi m\u1ecdi $x$<br\/>V\u1eady $x^2 - 6x + 12 > 0$ c\u00f3 nghi\u1ec7m v\u1edbi m\u1ecdi gi\u00e1 tr\u1ecb $x$<br\/>Ta ch\u1ecdn \u0111\u00e1p \u00e1n: <span class='basic_pink'>A. \u0110\u00fang<\/span><\/span> <br\/><\/span><br\/>","column":2}]}],"id_ques":1226},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai28/lv2/img\/3.jpg' \/><\/center><br\/>Gi\u1ea3i b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh $6x - 7 \\geq x + 23$","select":[" A. $\\left\\{x \\mid x \\geq 5 \\right\\}$"," B. $\\left\\{x \\mid x \\geq -5 \\right\\}$","C. $\\left\\{x \\mid x \\geq 6 \\right\\}$","D. $\\left\\{x \\mid \\geq -6 \\right\\}$"],"hint":"S\u1eed d\u1ee5ng quy t\u1eafc chuy\u1ec3n v\u1ebf v\u00e0 quy t\u1eafc nh\u00e2n v\u1edbi m\u1ed9t s\u1ed1 \u0111\u1ec3 gi\u1ea3i b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh.","explain":"<span class='basic_left'>Ta c\u00f3 $6x - 7 \\geq x + 23$<br\/>$\\Leftrightarrow 6x - x \\geq 23 + 7$<br\/>$\\Leftrightarrow 5x \\geq 30$<br\/>$\\Leftrightarrow x \\geq 30 : 5$ <br\/>$\\Leftrightarrow x \\geq 6$<br\/>V\u1eady t\u1eadp nghi\u1ec7m c\u1ee7a b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 $\\left\\{x \\mid x \\geq 6\\right\\}$ <br\/>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'>C. $\\left\\{x \\mid x \\geq 6 \\right\\}$<\/span><\/span>","column":2}]}],"id_ques":1227},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"<span class='basic_left'><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai28/lv2/img\/5.jpg' \/><\/center> B\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh $x^2 - 10x + 30 < 0$ c\u00f3 nghi\u1ec7m v\u1edbi m\u1ecdi $x$. <b>\u0110\u00fang<\/b> hay <b> Sai<\/b>?<\/span>","select":[" A. \u0110\u00fang"," B. Sai"],"hint":"","explain":"<span class='basic_left'><span class='basic_green'>Ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i:<\/span><br\/>Bi\u1ebfn \u0111\u1ed5i b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh v\u1ec1 d\u1ea1ng $\\left[f(x)\\right]^2 + k > 0$ (v\u1edbi $k > 0$)<\/span> <br\/><span class='basic_left'><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Ta c\u00f3: $x^2 - 10x + 30 = (x - 5)^2 + 5$<br\/>V\u00ec $(x - 5)^2 \\geq 0$ v\u1edbi m\u1ecdi $x$ n\u00ean $(x - 5)^2 + 5 \\geq 0$ v\u1edbi m\u1ecdi $x$ <br\/>V\u1eady $x^2 -10x + 30 < 0$ v\u00f4 nghi\u1ec7m<br\/>Ta ch\u1ecdn \u0111\u00e1p \u00e1n: <span class='basic_pink'>B. Sai<\/span><\/span> <br\/><\/span><br\/>","column":2}]}],"id_ques":1228},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"Gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh: $|3x + 2| = |4x - 5|$","select":[" A. $S = \\left\\{\\dfrac{-3}{7}; 7\\right\\}$"," B. $S = \\left\\{\\dfrac{3}{7}; 7\\right\\}$ ","C. $S = \\left\\{-3; 7\\right\\}$","D. $S = \\left\\{-3 ; -7\\right\\}$"],"hint":"$|A(x)| = |B(x)| \\Leftrightarrow A(x) = \\pm B(x)$ ","explain":"<span class='basic_left'>Ta c\u00f3:<br\/>$|3x + 2| = |4x - 5|$ <br\/>$\\Leftrightarrow \\left[\\begin{array}{l} 3x + 2 = 4x - 5\\\\ 3x + 2 = -(4x - 5)\\end{array} \\right.$<br\/>$\\Leftrightarrow \\left[\\begin{array}{l} 4x - 3x = 2 + 5\\\\3x + 2 = -4x + 5\\end{array} \\right.$<br\/>$\\Leftrightarrow \\left[\\begin{array}{l} x = 7\\\\ 3x + 4x = 5 - 2\\end{array} \\right.$<br\/>$\\Leftrightarrow \\left[\\begin{array}{l} x = 7 \\\\ 7x = 3\\end{array} \\right.$<br\/>$\\Leftrightarrow \\left[\\begin{array}{l} x = 7 \\\\ x = \\dfrac{3}{7}\\end{array} \\right.$<br\/>V\u1eady $S = \\left\\{\\dfrac{3}{7}; 7\\right\\}$<br\/><span class='basic_pink'>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 B <\/span><br\/> ","column":2}]}],"id_ques":1229},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai28/lv2/img\/7.jpg' \/><\/center><br\/>B\u1ecf d\u1ea5u gi\u00e1 tr\u1ecb tuy\u1ec7t \u0111\u1ed1i v\u00e0 r\u00fat g\u1ecdn bi\u1ec3u th\u1ee9c: $B = 15x + 30 - 2|2x - 1|$ v\u1edbi $x < 0$","select":[" $B = 11x + 28$ "," $B = 11x + 32$","$B = 19x + 28$","$B = 19x + 32$ "],"hint":"\u00c1p d\u1ee5ng \u0111\u1ecbnh ngh\u0129a gi\u00e1 tr\u1ecb tuy\u1ec7t \u0111\u1ed1i \u0111\u1ec3 r\u00fat g\u1ecdn: <br\/> $|x| = \\left\\{\\begin{array}{l} x \\hspace{0,2cm}\\text{n\u1ebfu } x \\geq 0\\\\-x \\hspace{0,2cm}\\text{n\u1ebfu } x < 0 \\end{array} \\right.$","explain":"<span class='basic_left'>Khi $x < 0$, ta c\u00f3 $2x - 1 < 0$ n\u00ean $|2x - 1| = - (2x - 1) = 1 - 2x$<br\/>V\u1eady<br\/>$B = 15x + 30 - 2|2x - 1| = 15x + 30 - 2(1 - 2x) = 15x + 30 - 2 + 4x = 19x + 28$<br\/>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'>$B = 19x + 28$<\/span><\/span>","column":2}]}],"id_ques":1230},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai28/lv2/img\/5.jpg' \/><\/center><br\/>Gi\u1ea3i b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh: $|3x - 2| < 2x + 3$","select":[" A. $1 < x < 5$ "," B. $-1 < x < 5$","C. $\\dfrac{-1}{5} < x < 5$","D. $\\dfrac{1}{5} < x < 5$ "],"hint":"$|A| < B \\Leftrightarrow -B < A < B$.","explain":"<span class='basic_left'>Ta c\u00f3: <br\/>$|3x - 2| < 2x + 3 $<br\/>$\\Leftrightarrow -2x - 3 < 3x - 2 < 2x + 3$<br\/>$\\Leftrightarrow$ $\\left\\{\\begin{array}{l} -2x - 3 < 3x - 2\\\\3x - 2 < 2x + 3 \\end{array} \\right.$ <br\/>$\\Leftrightarrow$ $\\left\\{\\begin{array}{l} -3 + 2 < 3x + 2x\\\\3x - 2x < 3 + 2 \\end{array} \\right.$<br\/>$\\Leftrightarrow$ $\\left\\{\\begin{array}{l} -1 < 5x\\\\x < 5 \\end{array} \\right.$<br\/>$\\Leftrightarrow$ $\\left\\{\\begin{array}{l} x > \\dfrac{-1}{5} \\\\x < 5 \\end{array} \\right.$<br\/>$\\Leftrightarrow 0 < x < 2$<br\/>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'>C. $\\dfrac{-1}{5} < x < 5$<\/span><\/span>","column":2}]}],"id_ques":1231},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":5,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai28/lv2/img\/5.jpg' \/><\/center><br\/>Gi\u1ea3i b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh: $|2x + 5| > x - 4$","select":[" A. $x < -9$ ho\u1eb7c $x <\\dfrac{-1}{3}$ "," B. $x > 9$ ho\u1eb7c $x <\\dfrac{1}{3}$","C. $x > -9$ ho\u1eb7c $x <\\dfrac{1}{5}$","D. $-9 < x <\\dfrac{-1}{3}$ "],"hint":"$|A| > |B| \\Leftrightarrow A > B$ ho\u1eb7c $A < -B$.","explain":"<span class='basic_left'>Ta c\u00f3: <br\/>$|2x + 5| > x - 4$<br\/>$\\Leftrightarrow$ $\\left[\\begin{array}{l} 2x + 5 > x - 4\\\\2x + 5 < -(x - 4) \\end{array} \\right.$ <br\/>$\\Leftrightarrow$ $\\left[\\begin{array}{l} 2x - x > -4 - 5\\\\2x + 5 < -x + 4 \\end{array} \\right.$<br\/>$\\Leftrightarrow$ $\\left[\\begin{array}{l} x > -9\\\\ 2x + x < 4 - 5 \\end{array} \\right.$<br\/>$\\Leftrightarrow$ $\\left[\\begin{array}{l} x > -9\\\\3x < -1 \\end{array} \\right.$<br\/>$\\Leftrightarrow$ $\\left[\\begin{array}{l} x > -9\\\\x < \\dfrac{-1}{3} \\end{array} \\right.$<br\/>V\u1eady nghi\u1ec7m c\u1ee7a b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 $-9 < x <\\dfrac{-1}{3}$<br\/><span class='basic_pink'>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 D<\/span> ","column":2}]}],"id_ques":1232},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai28/lv2/img\/3.jpg' \/><\/center><br\/>Gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh: $|2x - 1| - |3x + 4| = 6$ $\\hspace{0,5cm}$ $(1)$","select":[" $x = \\dfrac{-9}{5}$ v\u00e0 $x = 1$"," $x = \\dfrac{-9}{5}$ v\u00e0 $x = -11$","$S = \\left\\{\\varnothing\\right\\}$","$x = -11$ "],"hint":"","explain":"<span class='basic_left'>Ta c\u00f3 $2x - 1 = 0 \\Leftrightarrow x = \\dfrac{1}{2}$; $3x + 4 = 0 \\Leftrightarrow x = \\dfrac{-4}{3} $. Ta c\u00f3 b\u1ea3ng sau: <br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai28/lv2/img\/D8C4B4_TB101.png' \/><\/center><br\/><b>Tr\u01b0\u1eddng h\u1ee3p 1:<\/b> N\u1ebfu $x < \\dfrac{-4}{3}$ th\u00ec ph\u01b0\u01a1ng tr\u00ecnh (1) tr\u1edf th\u00e0nh:<br\/>$-2x + 1 - (-3x - 4) = 6$<br\/>$\\Leftrightarrow -2x + 1 + 3x + 4 = 6$<br\/>$\\Leftrightarrow x = 1$ (kh\u00f4ng th\u1ecfa m\u00e3n $x < \\dfrac{-4}{3}$)<br\/><b>Tr\u01b0\u1eddng h\u1ee3p 2:<\/b> N\u1ebfu $\\dfrac{-4}{3} \\leq x \\leq \\dfrac{1}{2}$ th\u00ec ph\u01b0\u01a1ng tr\u00ecnh (1) tr\u1edf th\u00e0nh:<br\/>$-2x + 1 - (3x + 4) = 6$<br\/>$\\Leftrightarrow -2x + 1 - 3x - 4 = 6$<br\/>$\\Leftrightarrow -5x = 9$<br\/>$\\Leftrightarrow x = \\dfrac{-9}{5} $ (kh\u00f4ng th\u1ecfa m\u00e3n $\\dfrac{-4}{3} \\leq x \\leq \\dfrac{1}{2}$)<br\/><b>Tr\u01b0\u1eddng h\u1ee3p 3:<\/b> N\u1ebfu $x \\geq \\dfrac{1}{2}$ ph\u01b0\u01a1ng tr\u00ecnh (1) tr\u1edf th\u00e0nh:<br\/> $2x - 1 - (3x + 4) = 6$<br\/>$ \\Leftrightarrow 2x - 1 - 3x - 4 = 6$<br\/>$\\Leftrightarrow x = -11$ (kh\u00f4ng th\u1ecfa m\u00e3n $x \\geq \\dfrac{1}{2}$)<br\/>V\u1eady ph\u01b0\u01a1ng tr\u00ecnh (1) v\u00f4 nghi\u1ec7m<br\/><span class='basic_pink'>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 $S = \\left\\{\\varnothing\\right\\}$<\/span><\/span>","column":2}]}],"id_ques":1233},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"Gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh: $||x + 4| - 3| = 8$","select":[" $S = \\left\\{ -7; -15\\right\\}$ "," $S = \\left\\{ -7; 15\\right\\}$","$S = \\left\\{ -15; 7\\right\\}$ ","$S = \\left\\{ 15\\right\\}$"],"hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/><b>B\u01b0\u1edbc 1: <\/b> T\u00ecm $|x + 4|$<br\/><b>B\u01b0\u1edbc 2:<\/b> T\u00ecm $x$<\/span> <br\/><span class='basic_left'><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Ta c\u00f3:<br\/>$||x + 4| - 3| = 8$ $\\Leftrightarrow \\left[\\begin{array}{l} |x + 4| - 3 = 8\\\\ |x + 4| - 3 = -8\\end{array} \\right.$ $\\Leftrightarrow \\left[\\begin{array}{l} |x + 4| = 11 \\hspace{0,2cm} \\text{(nh\u1eadn)} (1)\\\\ |x + 4| = -5 \\hspace{0,2cm} \\text{(lo\u1ea1i)}\\end{array} \\right.$<br\/>Gi\u1ea3i $(1)$ ta \u0111\u01b0\u1ee3c:<br\/> $|x + 4| = 11$ $\\Leftrightarrow \\left[\\begin{array}{l} x + 4 = 11\\\\ x + 4 = -11\\end{array} \\right.$ $\\Leftrightarrow \\left[\\begin{array}{l} x = 7\\\\ x = -15\\end{array} \\right.$<br\/>V\u1eady t\u1eadp nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 $S = \\left\\{ -15; 7\\right\\}$ <\/span><br\/><span class='basic_pink'>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 $S = \\left\\{ -15; 7\\right\\}$<\/span> <br\/><\/span><br\/>","column":2}]}],"id_ques":1234},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":"Gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh: $||2x - 3| + 9| = 24$","select":[" $S = \\left\\{ -6; 9\\right\\}$ "," $S = \\left\\{ -6; 6\\right\\}$","$S = \\left\\{ -9; -6\\right\\}$ ","$S = \\left\\{ 9\\right\\}$"],"hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/><b>B\u01b0\u1edbc 1: <\/b> T\u00ecm $|2x - 3|$<br\/><b>B\u01b0\u1edbc 2:<\/b> T\u00ecm $x$<\/span> <br\/><span class='basic_left'><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Ta c\u00f3:<br\/>$||2x - 3| + 9| = 24$ $\\Leftrightarrow \\left[\\begin{array}{l} |2x - 3| + 9 = 24\\\\ |2x - 3| + 9 = -24\\end{array} \\right.$ $\\Leftrightarrow \\left[\\begin{array}{l} |2x -3| = 15 \\hspace{0,2cm} \\text{(nh\u1eadn)} (1)\\\\ |2x - 3| = -33 \\hspace{0,2cm} \\text{(lo\u1ea1i)}\\end{array} \\right.$<br\/>Gi\u1ea3i $(1)$ ta \u0111\u01b0\u1ee3c:<br\/> $|2x - 3| = 15$ $\\Leftrightarrow \\left[\\begin{array}{l} 2x - 3 = 15\\\\ 2x - 3 = -15\\end{array} \\right.$ $\\Leftrightarrow \\left[\\begin{array}{l} 2x = 18\\\\ 2x = -12\\end{array} \\right.$ $\\Leftrightarrow \\left[\\begin{array}{l} x = 9\\\\ x = -6\\end{array} \\right.$<br\/>V\u1eady t\u1eadp nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 $S = \\left\\{ -6; 9\\right\\}$ <\/span><br\/><span class='basic_pink'>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 $S = \\left\\{ -6; 9\\right\\}$<\/span> <br\/><\/span><br\/>","column":2}]}],"id_ques":1235},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai28/lv2/img\/3.jpg' \/><\/center><br\/>Gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh: $|x + 5| + |2x + 3| = 12$ $\\hspace{0,5cm}$ $(1)$","select":[" $S = \\left\\{\\dfrac{-20}{3}; -10 \\right\\}$"," $S = \\left\\{\\dfrac{-20}{3}; \\dfrac{4}{3} \\right\\}$","$S = \\left\\{-10; \\dfrac{4}{3} \\right\\}$","$S = \\left\\{\\dfrac{-20}{3}; \\dfrac{4}{3}; -10 \\right\\}$ "],"hint":"","explain":"<span class='basic_left'>Ta c\u00f3 $x + 5 = 0 \\Leftrightarrow x = -5$; $2x + 3 = 0 \\Leftrightarrow x = \\dfrac{-3}{2} $. Ta c\u00f3 b\u1ea3ng sau: <br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai28/lv2/img\/D8C4B4_TB102.png' \/><\/center><br\/><b>Tr\u01b0\u1eddng h\u1ee3p 1:<\/b> N\u1ebfu $x < -5$ th\u00ec ph\u01b0\u01a1ng tr\u00ecnh (1) tr\u1edf th\u00e0nh:<br\/>$-x - 5 - 2x - 3 = 12$<br\/>$\\Leftrightarrow -3x = 20$<br\/>$\\Leftrightarrow x = \\dfrac{-20}{3}$ (th\u1ecfa m\u00e3n $x < -5$)<br\/><b>Tr\u01b0\u1eddng h\u1ee3p 2:<\/b> N\u1ebfu $-5 \\leq x \\leq \\dfrac{-3}{2}$ th\u00ec ph\u01b0\u01a1ng tr\u00ecnh (1) tr\u1edf th\u00e0nh:<br\/>$x + 5 - 2x - 3 = 12$<br\/>$\\Leftrightarrow x = -10$ (kh\u00f4ng th\u1ecfa m\u00e3n $-5 \\leq x \\leq \\dfrac{-3}{2}$)<br\/><b>Tr\u01b0\u1eddng h\u1ee3p 3:<\/b> N\u1ebfu $x \\geq \\dfrac{-3}{2}$ ph\u01b0\u01a1ng tr\u00ecnh (1) tr\u1edf th\u00e0nh:<br\/> $x + 5 + 2x + 3 = 12$<br\/>$ \\Leftrightarrow 3x = 4$<br\/>$\\Leftrightarrow x = \\dfrac{4}{3}$ ( th\u1ecfa m\u00e3n $x \\geq \\dfrac{-3}{2}$)<br\/>V\u1eady ph\u01b0\u01a1ng tr\u00ecnh (1) c\u00f3 t\u1eadp nghi\u1ec7m l\u00e0 $S = \\left\\{\\dfrac{-20}{3}; \\dfrac{4}{3} \\right\\}$<br\/><span class='basic_pink'>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 $S = \\left\\{\\dfrac{-20}{3}; \\dfrac{4}{3} \\right\\}$<\/span><\/span>","column":2}]}],"id_ques":1236},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":"B\u1ecf d\u1ea5u gi\u00e1 tr\u1ecb tuy\u1ec7t \u0111\u1ed1i c\u1ee7a bi\u1ec3u th\u1ee9c $|5x - 12|$ ta \u0111\u01b0\u1ee3c bi\u1ec3u th\u1ee9c:","select":[" A. $5x - 12$ n\u1ebfu $x \\geq 0$ v\u00e0 $-5x + 12$ n\u1ebfu $x < 0$ "," B. $5x - 12$ n\u1ebfu $x \\geq 0$ v\u00e0 $-5x - 12$ n\u1ebfu $x < 0$","C. $5x - 12$ n\u1ebfu $x \\geq \\dfrac{12}{5}$ v\u00e0 $-5x + 12$ n\u1ebfu $x < \\dfrac{12}{5}$ ","D. $5x - 12$ n\u1ebfu $x \\geq \\dfrac{12}{5}$ v\u00e0 $-5x - 12$ n\u1ebfu $x < \\dfrac{12}{5}$"],"hint":"","explain":"<span class='basic_left'>+ N\u1ebfu $5x - 12 \\geq 0 \\Leftrightarrow x \\geq \\dfrac{12}{5}$ th\u00ec $|5x - 12| = 5x - 12$<br\/>+ N\u1ebfu $5x - 12 < 0 \\Leftrightarrow x < \\dfrac{12}{5}$ th\u00ec $|5x - 12| = -5x + 12$<br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'>C. $5x - 12$ n\u1ebfu $x \\geq \\dfrac{12}{5}$ v\u00e0 $-5x + 12$ n\u1ebfu $x < \\dfrac{12}{5}$<\/span><\/span>","column":1}]}],"id_ques":1237},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai28/lv2/img\/3.jpg' \/><\/center><br\/>Gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh: $|4x - 5| - 2x = -3x + 18$","select":[" $S = \\left\\{ \\dfrac{-23}{3}; \\dfrac{23}{5}\\right\\}$"," $S = \\left\\{ \\dfrac{-13}{3}; \\dfrac{23}{5}\\right\\}$","$S = \\left\\{ \\dfrac{-13}{3}\\right\\}$","$S = \\left\\{ \\dfrac{13}{3}; \\dfrac{23}{5}\\right\\}$ "],"hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/><b>B\u01b0\u1edbc 1:<\/b> B\u1ecf d\u1ea5u gi\u00e1 tr\u1ecb tuy\u1ec7t \u0111\u1ed1i<br\/><b>B\u01b0\u1edbc 2:<\/b> Gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh \u0111\u1ec3 t\u00ecm nghi\u1ec7m<\/span> <br\/><span class='basic_left'><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>+ V\u1edbi $x \\geq \\dfrac{5}{4}$ ta c\u00f3:<br\/>$|4x - 5| - 2x = -3x + 18 \\\\ \\Leftrightarrow 4x - 5 - 2x = -3x + 18 \\\\ \\Leftrightarrow 2x - 5 = -3x + 18 \\\\ \\Leftrightarrow 2x + 3x = 18 + 5 \\\\ \\Leftrightarrow 5x = 23 \\\\ \\Leftrightarrow x = \\dfrac{23}{5} \\text{(nh\u1eadn)}$ <br\/>+ V\u1edbi $x < \\dfrac{5}{4}$ ta c\u00f3: <br\/>$|4x - 5| - 2x = -3x + 18 \\\\ \\Leftrightarrow -4x + 5 - 2x = -3x + 18 \\\\ \\Leftrightarrow -6x + 5 = -3x + 18 \\\\ \\Leftrightarrow -6x + 3x = 18 - 5 \\\\ \\Leftrightarrow -3x = 13 \\\\ \\Leftrightarrow x = \\dfrac{-13}{3} \\text{(nh\u1eadn)}$<br\/>V\u1eady $S = \\left\\{ \\dfrac{-13}{3}; \\dfrac{23}{5}\\right\\}$<br\/>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0: <span class='basic_pink'>$S = \\left\\{ \\dfrac{-13}{3}; \\dfrac{23}{5}\\right\\}$<\/span><br\/><span class='basic_left'><span class='basic_green'>Nh\u1eadn x\u00e9t:<\/span><br\/><b>C\u00e1ch gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh d\u1ea1ng $|A(x)| = B(x)$ (*)<\/b><br\/>+ $A(x) \\geq 0$ (1) th\u00ec (*) tr\u1edf th\u00e0nh: $A(x) = B(x)$ (2)<br\/>Gi\u1ea3i (2) v\u00e0 ch\u1ecdn nghi\u1ec7m th\u1ecfa (1) ta \u0111\u01b0\u1ee3c nghi\u1ec7m c\u1ee7a (*)<br\/>+ $A(x) < 0$ (3) th\u00ec (*) tr\u1edf th\u00e0nh: $-A(x) = B(x)$ (4)<br\/>Gi\u1ea3i (4) v\u00e0 ch\u1ecdn nghi\u1ec7m th\u1ecfa (3) ta \u0111\u01b0\u1ee3c nghi\u1ec7m c\u1ee7a (*)<br\/>+ K\u1ebft lu\u1eadn: Nghi\u1ec7m c\u1ee7a (*) l\u00e0 t\u1ea5t c\u1ea3 c\u00e1c nghi\u1ec7m v\u1eeba t\u00ecm \u0111\u01b0\u1ee3c \u1edf c\u00e1c tr\u01b0\u1eddng h\u1ee3p tr\u00ean. <\/span> <br\/>","column":2}]}],"id_ques":1238},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank_random","correct":[[["4x + 7","7 + 4x"]]],"list":[{"point":5,"width":50,"content":"","type_input":"","ques":"N\u1ebfu $x > 0$ th\u00ec $|4x + 7| =$ <span class='basic_hoi_black'>?<\/span><br\/><b>\u0110\u00e1p \u00e1n:<\/b> $|4x + 7| = $ _input_ ","hint":"","explain":"<span class='basic_left'>Khi $x > 0$, ta c\u00f3 $4x > 0 \\Rightarrow 4x + 7 > 0$ n\u00ean $|4x + 7| = 4x + 7$<br\/>V\u1eady \u0111\u00e1p \u00e1n c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 <span class='basic_pink'>$4x + 7$<\/span><\/span>"}]}],"id_ques":1239},{"time":24,"part":[{"title":"\u0110i\u1ec1n \u0111\u00e1p \u00e1n th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng","title_trans":"","temp":"fill_the_blank","correct":[[["x"],["2x"],["3"]]],"list":[{"point":5,"width":50,"content":"","type_input":"","ques":"B\u1ecf d\u1ea5u gi\u00e1 tr\u1ecb tuy\u1ec7t \u0111\u1ed1i c\u1ee7a bi\u1ec3u th\u1ee9c: $|x^2 - 2x + 3| $ <br\/><b>\u0110\u00e1p \u00e1n:<\/b> $|x^2 - 2x + 3| = \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}^2 - \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{} + \\FormInput[40][bl_elm_true basic_elm basic_blank basic_blank_part]{}$ ","hint":"","explain":"<span class='basic_left'>Ta c\u00f3:<br\/>$x^2 - 2x + 3 = (x - 1)^2 + 2 \\geq 2 \\hspace{0,2cm} \\forall x$<br\/>$\\Rightarrow |x^2 - 2x + 3| = x^2 - 2x + 3$<br\/>V\u1eady c\u00e1c \u0111\u00e1p \u00e1n c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u1ea7n l\u01b0\u1ee3t l\u00e0 <span class='basic_pink'> $x ; 2x; 3$<\/span><\/span>"}]}],"id_ques":1240}],"lesson":{"save":0,"level":2}}