{"segment":[{"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: $|2x + 1| = |5x - 5|$","select":[" A. $S = \\left\\{\\dfrac{-4}{7}; 2\\right\\}$"," B. $S = \\left\\{\\dfrac{4}{7}; 2\\right\\}$ ","C. $S = \\left\\{-4; 2\\right\\}$","D. $S = \\left\\{-2 ; -4\\right\\}$"],"hint":"$|A(x)| = |B(x)| \\Leftrightarrow A(x) = \\pm B(x)$ ","explain":"<span class='basic_left'>Ta c\u00f3:<br\/>$|2x + 1| = |5x - 5|$ <br\/>$\\Leftrightarrow \\left[\\begin{array}{l} 2x + 1 = 5x - 5\\\\ 2x + 1 = -(5x - 5)\\end{array} \\right.$<br\/>$\\Leftrightarrow \\left[\\begin{array}{l} 5x - 2x = 1 + 5\\\\2x + 1 = -5x + 5\\end{array} \\right.$<br\/>$\\Leftrightarrow \\left[\\begin{array}{l} 3x = 6\\\\ 2x + 5x = 5 - 1\\end{array} \\right.$<br\/>$\\Leftrightarrow \\left[\\begin{array}{l} x = 6 : 3 \\\\ 7x = 4\\end{array} \\right.$<br\/>$\\Leftrightarrow \\left[\\begin{array}{l} x = 2 \\\\ x = \\dfrac{4}{7}\\end{array} \\right.$<br\/>V\u1eady $S = \\left\\{\\dfrac{4}{7}; 2\\right\\}$<br\/><span class='basic_pink'>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 B <\/span><br\/> ","column":2}]}],"id_ques":1171},{"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: $|-3x + 2| = |x - 6|$","select":[" A. $S = \\left\\{-2; 2\\right\\}$"," B. $S = \\left\\{2; 2\\right\\}$ ","C. $S = \\left\\{-4; 2\\right\\}$","D. $S = \\left\\{-2 ; -4\\right\\}$"],"hint":"$|A(x)| = |B(x)| \\Leftrightarrow A(x) = \\pm B(x)$ ","explain":"<span class='basic_left'>Ta c\u00f3:<br\/>$|-3x + 2| = |x - 6|$ <br\/><br\/>$\\Leftrightarrow \\left[\\begin{array}{l} -3x + 2 = x - 6\\\\ -3x + 2 = -(x - 6)\\end{array} \\right.$<br\/>$\\Leftrightarrow \\left[\\begin{array}{l} x + 3x = 2 + 6\\\\-3x + 2 = -x + 6\\end{array} \\right.$<br\/>$\\Leftrightarrow \\left[\\begin{array}{l} 4x = 8\\\\ -3x + x = 6 - 2\\end{array} \\right.$<br\/>$\\Leftrightarrow \\left[\\begin{array}{l} x = 2 \\\\ -2x = 4\\end{array} \\right.$<br\/>$\\Leftrightarrow \\left[\\begin{array}{l} x = 2 \\\\ x =-2\\end{array} \\right.$<br\/><br\/>V\u1eady t\u1eadp nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 $S = \\left\\{-2; 2\\right\\}$<br\/><span class='basic_pink'>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 A <\/span><br\/> ","column":2}]}],"id_ques":1172},{"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/bai27/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: $B = 12x + 52 - 2|x - 1|$ v\u1edbi $x < 0$","select":[" $B = 14x + 54$ "," $B = 14x + 50$","$B = 12x + 50$","$B = 12x + 54$ "],"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 $x - 1 < 0$ n\u00ean $|x - 1| = - (x - 1) = 1 - x$<br\/>V\u1eady<br\/>$B = 12x + 52 - 2|x - 1| = 12x + 52 - 2(1 - x) = 12x + 52 - 2 + 2x = 14x + 50$<br\/>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'>$B = 14x + 50$<\/span><\/span>","column":2}]}],"id_ques":1173},{"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/bai27/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: $A = 15- |3x + 5| -2(x - 8)$ v\u1edbi $x > 0$","select":[" $A = 26 + 5x$ "," $A = 26 - 5x$","$A = 5x - 26$","$A = -5x - 26$ "],"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 $3x + 5 > 0$ n\u00ean $|3x + 5| = 3x + 5$<br\/>V\u1eady<br\/>$ \\begin{align*}A&=15- |3x + 5| -2(x - 8) \\\\&= 15 - (3x + 5) - 2x + 16 \\\\&= 15 - 3x - 5 - 2x + 16\\\\&= 26 - 5x\\end{align*} $<br\/>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'>$A = 26 - 5x$<\/span><\/span>","column":2}]}],"id_ques":1174},{"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/bai27/lv2/img\/5.jpg' \/><\/center><br\/>Gi\u1ea3i b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh: $|2x - 1| < x + 1$","select":[" A. $0 < x < 1$ "," B. $-2 < x < 2$","C. $0 < x < 2$","D. $x < 2$ "],"hint":"$|A| < B \\Leftrightarrow -B < A < B$.","explain":"<span class='basic_left'>Ta c\u00f3: <br\/>$|2x - 1| < x + 1 $<br\/>$\\Leftrightarrow -x - 1 < 2x - 1 < x + 1$<br\/>$\\Leftrightarrow$ $\\left\\{\\begin{array}{l} -x - 1 < 2x - 1\\\\2x - 1 < x + 1 \\end{array} \\right.$ <br\/>$\\Leftrightarrow$ $\\left\\{\\begin{array}{l} -1 + 1 < 2x + x\\\\2x - x < 1 + 1 \\end{array} \\right.$<br\/>$\\Leftrightarrow$ $\\left\\{\\begin{array}{l} 0 < 3x\\\\x < 2 \\end{array} \\right.$<br\/>$\\Leftrightarrow$ $\\left\\{\\begin{array}{l} x > 0\\\\x < 2 \\end{array} \\right.$<br\/>$\\Leftrightarrow 0 < x < 2$<br\/>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'>C. $0 < x < 2$<\/span><\/span>","column":2}]}],"id_ques":1175},{"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/bai27/lv2/img\/5.jpg' \/><\/center><br\/>Gi\u1ea3i b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh: $|3x + 2| > 2x - 1$","select":[" A. $x < -3$ ho\u1eb7c $x <\\dfrac{-1}{5}$ "," B. $x > 3$ ho\u1eb7c $x <\\dfrac{1}{5}$","C. $x > -3$ ho\u1eb7c $x <\\dfrac{1}{5}$","D. $x > -3$ ho\u1eb7c $x <\\dfrac{-1}{5}$ "],"hint":"$|A| > B \\Leftrightarrow A > B$ ho\u1eb7c $A < -B$.","explain":"<span class='basic_left'>Ta c\u00f3: <br\/>$|3x + 2| > 2x - 1$<br\/>$\\Leftrightarrow$ $\\left[\\begin{array}{l} 3x + 2 > 2x - 1\\\\3x + 2 < -(2x - 1) \\end{array} \\right.$ <br\/>$\\Leftrightarrow$ $\\left[\\begin{array}{l} 3x - 2x > -1 - 2\\\\3x + 2 < -2x + 1 \\end{array} \\right.$<br\/>$\\Leftrightarrow$ $\\left[\\begin{array}{l} x > -3\\\\ 3x + 2x < 1 - 2 \\end{array} \\right.$<br\/>$\\Leftrightarrow$ $\\left[\\begin{array}{l} x > -3\\\\5x < -1 \\end{array} \\right.$<br\/>$\\Leftrightarrow$ $\\left[\\begin{array}{l} x > -3\\\\x < \\dfrac{-1}{5} \\end{array} \\right.$<br\/>V\u1eady nghi\u1ec7m c\u1ee7a b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 $x > -3$ ho\u1eb7c $x <\\dfrac{-1}{5}$<br\/><span class='basic_pink'>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 D<\/span> ","column":2}]}],"id_ques":1176},{"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":[[["3x + 8"],"8 + 3x"]],"list":[{"point":5,"width":50,"content":"","type_input":"","ques":"N\u1ebfu $x > 0$ th\u00ec $|3x + 8| =$ <span class='basic_hoi_black'>?<\/span><br\/><b>\u0110\u00e1p \u00e1n:<\/b> $|3x + 8| = $ _input_ ","hint":"","explain":"<span class='basic_left'>Khi $x > 0$, ta c\u00f3 $3x > 0 \\Rightarrow 3x + 8 > 0$ n\u00ean $|3x + 8| = 3x + 8$<br\/>V\u1eady \u0111\u00e1p \u00e1n c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 <span class='basic_pink'>$3x + 8$<\/span><\/span>"}]}],"id_ques":1177},{"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":[[["-5x + 4","4 - 5x"]]],"list":[{"point":5,"width":50,"content":"","type_input":"","ques":"N\u1ebfu $x < 0$ th\u00ec $|-5x + 4| =$ <span class='basic_hoi_black'>?<\/span><br\/><b>\u0110\u00e1p \u00e1n:<\/b> $|-5x + 4| = $ _input_ ","hint":"","explain":"<span class='basic_left'>Khi $x < 0$, ta c\u00f3 $-5x > 0 \\Rightarrow -5x + 4 > 0$ n\u00ean $|-5x + 4| = -5x + 4$<br\/>V\u1eady \u0111\u00e1p \u00e1n c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 <span class='basic_pink'>$-5x + 4$<\/span><\/span>"}]}],"id_ques":1178},{"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":[[["-7x + 12","12 - 7x"]]],"list":[{"point":5,"width":50,"content":"","type_input":"","ques":"N\u1ebfu $x < 0$ th\u00ec $|7x - 12| =$ <span class='basic_hoi_black'>?<\/span><br\/><b>\u0110\u00e1p \u00e1n:<\/b> $|7x - 12| = $ _input_ ","hint":"","explain":"<span class='basic_left'>Khi $x < 0$, ta c\u00f3 $7x < 0 \\Rightarrow 7x - 12 < 0$ n\u00ean $|7x - 12| = -(7x - 12) = -7x + 12$<br\/>V\u1eady \u0111\u00e1p \u00e1n c\u1ea7n \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng l\u00e0 <span class='basic_pink'>$-7x + 12$<\/span><\/span>"}]}],"id_ques":1179},{"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":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai27/lv2/img\/5.jpg' \/><\/center><br\/>Gi\u1ea3i b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh: $|x + 8| < 2x + 4$","select":[" A. $x > 4$ "," B. $x > -4$","C. $x < 4$","D. $x < -4$ "],"hint":"$|A| < B \\Leftrightarrow -B < A < B$.","explain":"<span class='basic_left'>Ta c\u00f3: <br\/>$|x + 8| < 2x + 4 $<br\/>$\\Leftrightarrow -2x - 4 < x + 8 < 2x + 4$<br\/>$\\Leftrightarrow$ $\\left\\{\\begin{array}{l} -2x - 4 < x + 8 \\\\ x + 8 < 2x + 4 \\end{array} \\right.$ <br\/>$\\Leftrightarrow$ $\\left\\{\\begin{array}{l} -2x - x < 8 + 4\\\\2x - x > 8 - 4 \\end{array} \\right.$<br\/>$\\Leftrightarrow$ $\\left\\{\\begin{array}{l} -3x < 12\\\\x > 4 \\end{array} \\right.$<br\/>$\\Leftrightarrow$ $\\left\\{\\begin{array}{l} x >-4\\\\x > 4 \\end{array} \\right.$<br\/>$\\Leftrightarrow x > 4$<br\/>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'>A. $x > 4$<\/span><\/span>","column":2}]}],"id_ques":1180},{"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":"Gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh: $|x + 3| = |2x - 6|$","select":[" A. $S = \\left\\{\\dfrac{-9}{4}; 9\\right\\}$"," B. $S = \\left\\{\\dfrac{9}{4}; 9\\right\\}$ ","C. $S = \\left\\{-1; 9\\right\\}$","D. $S = \\left\\{1; 9\\right\\}$"],"hint":"$|A(x)| = |B(x)| \\Leftrightarrow A(x) = \\pm B(x)$ ","explain":"<span class='basic_left'>Ta c\u00f3:<br\/>$|x + 3| = |2x - 6|$ <br\/>$\\Leftrightarrow \\left[\\begin{array}{l} x + 3 = 2x - 6\\\\ x + 3 = -(2x - 6)\\end{array} \\right.$<br\/>$\\Leftrightarrow \\left[\\begin{array}{l} 2x - x = 3 + 6\\\\x + 3 = -2x + 6\\end{array} \\right.$<br\/>$\\Leftrightarrow \\left[\\begin{array}{l} x = 9\\\\ x + 2x = 6 - 3\\end{array} \\right.$<br\/>$\\Leftrightarrow \\left[\\begin{array}{l} x = 9 \\\\ 3x = 3\\end{array} \\right.$<br\/>$\\Leftrightarrow \\left[\\begin{array}{l} x = 9 \\\\ x = 1 \\end{array} \\right.$<br\/>V\u1eady $S = \\left\\{1; 9\\right\\}$<br\/><span class='basic_pink'>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 D <\/span><br\/> ","column":2}]}],"id_ques":1181},{"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/bai27/lv2/img\/2.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: $A = |3x - 8| - 6(x - 2)$ v\u1edbi $x < 0$","select":[" $A = 9x - 20$ "," $A = 20 + 9x$","$A = 20 - 9x$","$A = -20 - 9x$ "],"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 $3x < 0 \\Rightarrow 3x - 8 < 0$ n\u00ean $|3x - 8| = - (3x - 8) = 8 - 3x$<br\/>V\u1eady<br\/>$A = |3x - 8| - 6(x - 2) = 8 - 3x - 6x + 12 = 20 - 9x$<br\/>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'>$A = 20 - 9x$<\/span><\/span>","column":2}]}],"id_ques":1182},{"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/bai27/lv2/img\/5.jpg' \/><\/center><br\/>Gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh: $|5x| = 3x - 16$","select":[" $S = \\left\\{ -2; 8\\right\\}$"," $S = \\left\\{ -8; -2\\right\\}$","$S = \\left\\{ -8; 2\\right\\}$","$S = \\varnothing$ "],"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 $x \\geq 0$ ta c\u00f3:<br\/>$|5x| = 3x - 16 \\Leftrightarrow 5x = 3x - 16 \\Leftrightarrow 5x - 3x = -16 \\Leftrightarrow 2x = -16 \\Leftrightarrow x = -8 $ (lo\u1ea1i)<br\/>+ V\u1edbi $x < 0$ ta c\u00f3: <br\/>$|5x| = 3x - 16 \\Leftrightarrow -5x = 3x - 16 \\Leftrightarrow -5x - 3x = -16 \\Leftrightarrow -8x = -16 \\Leftrightarrow x = 2 $ (lo\u1ea1i)<br\/>V\u1eady $S = \\varnothing$<br\/>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0: <span class='basic_pink'>$S = \\varnothing$<\/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":1183},{"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/bai27/lv2/img\/4.jpg' \/><\/center><br\/>Gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh: $|5x - 1| + 2x = 8x - 3$","select":[" $S = \\left\\{ -2\\right\\}$"," $S = \\left\\{ 2\\right\\}$","$S = \\left\\{ \\dfrac{4}{11}; 2\\right\\}$","$S = \\left\\{ \\dfrac{4}{5}; 2\\right\\}$ "],"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 $x \\geq \\dfrac{1}{5}$ ta c\u00f3:<br\/>$|5x - 1| + 2x = 8x - 3 \\\\ \\Leftrightarrow 5x - 1 + 2x = 8x - 3 \\\\ \\Leftrightarrow 7x - 1 = 8x - 3 \\\\ \\Leftrightarrow 8x - 7x = -1 + 3 \\\\ \\Leftrightarrow x = 2 $ (nh\u1eadn)<br\/>+ V\u1edbi $x < \\dfrac{1}{5}$ ta c\u00f3: <br\/>$|5x - 1| + 2x = 8x - 3 \\\\ \\Leftrightarrow -5x + 1 + 2x = 8x - 3 \\\\ \\Leftrightarrow -3x + 1 = 8x - 3 \\\\ \\Leftrightarrow 8x + 3x = 1 + 3 \\\\ \\Leftrightarrow 11x = 4 \\\\ \\Leftrightarrow x = \\dfrac{4}{11}$ (lo\u1ea1i)<br\/>V\u1eady $S = \\left\\{ 2\\right\\}$<br\/>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0: <span class='basic_pink'>$S = \\left\\{ 2\\right\\}$<\/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":1184},{"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/bai27/lv2/img\/3.jpg' \/><\/center><br\/>Gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh: $|8x - 4| - 2x = -3x + 14$","select":[" $S = \\left\\{ -2\\right\\}$"," $S = \\left\\{ 2\\right\\}$","$S = \\left\\{ \\dfrac{-10}{7}; 2\\right\\}$","$S = \\left\\{ \\dfrac{7}{10}; 2\\right\\}$ "],"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 $x \\geq \\dfrac{1}{2}$ ta c\u00f3:<br\/>$|8x - 4| - 2x = -3x + 14 \\\\ \\Leftrightarrow 8x - 4 - 2x = -3x + 14 \\\\ \\Leftrightarrow 6x - 4 = -3x + 14 \\\\ \\Leftrightarrow 6x + 3x = 14 + 4 \\\\ \\Leftrightarrow 9x = 18 \\\\ \\Leftrightarrow x = 2$ (nh\u1eadn)<br\/>+ V\u1edbi $x < \\dfrac{1}{2}$ ta c\u00f3: <br\/>$|8x - 4| - 2x = -3x + 14 \\\\ \\Leftrightarrow -8x + 4 - 2x = -3x + 14 \\\\ \\Leftrightarrow -10x + 4 = -3x + 14 \\\\ \\Leftrightarrow -10x + 3x = 14 - 4 \\\\ \\Leftrightarrow -7x = 10 \\\\ \\Leftrightarrow x = \\dfrac{-10}{7}$ (nh\u1eadn)<br\/>V\u1eady $S = \\left\\{ \\dfrac{-10}{7}; 2\\right\\}$<br\/>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0: <span class='basic_pink'>$S = \\left\\{ \\dfrac{-10}{7}; 2\\right\\}$<\/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":1185},{"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 $|3x - 12|$ ta \u0111\u01b0\u1ee3c bi\u1ec3u th\u1ee9c:","select":[" A. $3x - 12$ n\u1ebfu $x \\geq 0$ v\u00e0 $-3x + 12$ n\u1ebfu $x < 0$ "," B. $3x - 12$ n\u1ebfu $x \\geq 0$ v\u00e0 $-3x - 12$ n\u1ebfu $x < 0$","C. $3x - 12$ n\u1ebfu $x \\geq 4$ v\u00e0 $-3x + 12$ n\u1ebfu $x < 4$ ","D. $3x - 12$ n\u1ebfu $x \\geq 4$ v\u00e0 $-3x - 12$ n\u1ebfu $x < 4$"],"hint":"","explain":"<span class='basic_left'>+ N\u1ebfu $3x - 12 \\geq 0 \\Leftrightarrow x \\geq 4$ th\u00ec $|3x - 12| = 3x - 12$<br\/>+ N\u1ebfu $3x - 12 < 0 \\Leftrightarrow x < 4$ th\u00ec $|3x - 12| = -3x + 12$<br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'>C. $3x - 12$ n\u1ebfu $x \\geq 4$ v\u00e0 $-3x + 12$ n\u1ebfu $x < 4$<\/span><\/span>","column":1}]}],"id_ques":1186},{"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":"B\u1ecf d\u1ea5u gi\u00e1 tr\u1ecb tuy\u1ec7t \u0111\u1ed1i c\u1ee7a bi\u1ec3u th\u1ee9c $|-4x + 10|$ ta \u0111\u01b0\u1ee3c bi\u1ec3u th\u1ee9c:","select":[" A. $-4x + 10$ n\u1ebfu $x \\geq 0$ v\u00e0 $-4x - 10$ n\u1ebfu $x < 0$ "," B. $-4x + 10$ n\u1ebfu $x \\geq 0$ v\u00e0 $4x - 10$ n\u1ebfu $x < 0$","C. $4x + 10$ n\u1ebfu $x \\geq \\dfrac{5}{2}$ v\u00e0 $4x - 10$ n\u1ebfu $x < \\dfrac{5}{2}$ ","D. $-4x + 10$ n\u1ebfu $x \\leq \\dfrac{5}{2}$ v\u00e0 $4x - 10$ n\u1ebfu $x > \\dfrac{5}{2}$"],"hint":"","explain":"<span class='basic_left'>+ N\u1ebfu $-4x + 10 \\geq 0 \\Leftrightarrow x \\leq \\dfrac{5}{2}$ th\u00ec $|-4x + 10| = -4x + 10$<br\/>+ N\u1ebfu $-4x + 10 < 0 \\Leftrightarrow x > \\dfrac{5}{2}$ th\u00ec $|-4x + 10| = 4x - 10$<br\/>V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 <span class='basic_pink'>D. $-4x + 10$ n\u1ebfu $x \\geq \\dfrac{5}{2}$ v\u00e0 $4x - 10$ n\u1ebfu $x < \\dfrac{5}{2}$<\/span><\/span>","column":1}]}],"id_ques":1187},{"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":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai27/lv2/img\/3.jpg' \/><\/center><br\/>Gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh: $|3x - 1| - |2x + 5| = 4$ $\\hspace{0,5cm}$ $(1)$","select":[" $x = \\dfrac{-8}{5}$ v\u00e0 $x = 10$"," $x = \\dfrac{-8}{5}$ v\u00e0 $x = 2$","$x = 2$ v\u00e0 $x = 10$","$x = \\dfrac{-8}{5}$; $x = 2$ v\u00e0 $x = 10$ "],"hint":"","explain":"<span class='basic_left'>Ta c\u00f3 $3x - 1 = 0 \\Leftrightarrow x = \\dfrac{1}{3}$; $2x + 5 = 0 \\Leftrightarrow x = \\dfrac{-5}{2} $. Ta c\u00f3 b\u1ea3ng sau: <br\/> <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai27/lv2/img\/D8C4B3_D101.png' \/><\/center><br\/>V\u1eady ph\u01b0\u01a1ng tr\u00ecnh (1) c\u00f3 hai nghi\u1ec7m $x = \\dfrac{-8}{5}$ v\u00e0 $x = 10$<br\/><span class='basic_pink'>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 A<\/span><\/span>","column":2}]}],"id_ques":1188},{"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: $||x + 1| - 2| = 4$","select":[" $S = \\left\\{ -7; -5\\right\\}$ "," $S = \\left\\{ -7; 5\\right\\}$","$S = \\left\\{ 7; -5\\right\\}$ ","$S = \\left\\{ 5; 7\\right\\}$"],"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 $|x + 1|$<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\/>$||x + 1| - 2| = 4$ $\\Leftrightarrow \\left[\\begin{array}{l} |x + 1| - 2 = 4\\\\ |x + 1| - 2 = -4\\end{array} \\right.$ $\\Leftrightarrow \\left[\\begin{array}{l} |x + 1| = 6 \\hspace{0,2cm} \\text{(nh\u1eadn)} (1)\\\\ |x + 1| = -2 \\hspace{0,2cm} \\text{(lo\u1ea1i)}\\end{array} \\right.$<br\/>Gi\u1ea3i $(1)$ ta \u0111\u01b0\u1ee3c:<br\/> $|x + 1| = 6$ $\\Leftrightarrow \\left[\\begin{array}{l} x + 1 = 6\\\\ x + 1 = -6\\end{array} \\right.$ $\\Leftrightarrow \\left[\\begin{array}{l} x = 5\\\\ x = -7\\end{array} \\right.$<br\/>V\u1eady t\u1eadp nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 $S = \\left\\{ -7; 5\\right\\}$ <\/span><br\/><span class='basic_pink'>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 $S = \\left\\{ -7; 5\\right\\}$<\/span> <br\/><\/span><br\/>","column":2}]}],"id_ques":1189},{"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: $||x + 4| - 3| = 15$","select":[" $S = \\left\\{ 12; 14\\right\\}$ "," $S = \\left\\{ -22; -14\\right\\}$","$S = \\left\\{ -22; 14\\right\\}$ ","$S = \\left\\{ -12; 14\\right\\}$"],"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\/>$||x + 4| - 3| = 15$ $\\Leftrightarrow \\left[\\begin{array}{l} |x + 4| - 3 = 15\\\\ |x + 4| - 3 = -15\\end{array} \\right.$ $\\Leftrightarrow \\left[\\begin{array}{l} |x + 4| = 18 \\hspace{0,2cm} \\text{(nh\u1eadn)} (1)\\\\ |x + 4| = -12 \\hspace{0,2cm} \\text{(lo\u1ea1i)}\\end{array} \\right.$<br\/>Gi\u1ea3i $(1)$ ta \u0111\u01b0\u1ee3c:<br\/> $|x + 4| = 18$ $\\Leftrightarrow \\left[\\begin{array}{l} x + 4 = 18\\\\ x + 4 = -18\\end{array} \\right.$ $\\Leftrightarrow \\left[\\begin{array}{l} x = 14\\\\ x = -22\\end{array} \\right.$<br\/>V\u1eady t\u1eadp nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 $S = \\left\\{ -22; 14\\right\\}$ <\/span><br\/><span class='basic_pink'>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 $S = \\left\\{ -22; 14\\right\\}$<\/span> <br\/><\/span><br\/>","column":2}]}],"id_ques":1190}],"lesson":{"save":0,"level":2}}