{"segment":[{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":10,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai27/lv3/img\/5.jpg' \/><\/center><br\/>Gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh: $x^2 - 5|x| + 6 = 0$","select":[" $S = \\left\\{-3; -2; 2; 3\\right\\}$"," $S = \\left\\{-2; 3\\right\\}$","$S = \\left\\{-3; -2\\right\\}$","$S = \\left\\{2; 3\\right\\}$"],"hint":"B\u1ecf d\u1ea5u gi\u00e1 tr\u1ecb tuy\u1ec7t \u0111\u1ed1i r\u1ed3i gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh.","explain":"<span class='basic_left'>+ V\u1edbi $x \\geq 0$ th\u00ec:<br\/>$x^2 - 5|x| + 6 = 0$ <br\/>$\\Leftrightarrow x^2 - 5x + 6 = 0$<br\/>$\\Leftrightarrow x^2 - 2x - 3x + 6 = 0$<br\/>$\\Leftrightarrow x(x - 2) - 3(x - 2) = 0$<br\/>$\\Leftrightarrow (x - 2)(x - 3) = 0$<br\/>$\\Leftrightarrow$ $\\left[\\begin{array}{l} x - 2 = 0\\\\ x - 3 = 0\\end{array} \\right.$<br\/>$\\Leftrightarrow$ $\\left[\\begin{array}{l} x = 2\\\\ x = 3\\end{array} \\right.$ (nh\u1eadn)<br\/>+ V\u1edbi $x < 0$ th\u00ec: <br\/>$x^2 - 5|x| + 6 = 0$ <br\/>$\\Leftrightarrow x^2 + 5x + 6 = 0$<br\/>$\\Leftrightarrow x^2 + 2x + 3x + 6 = 0$<br\/>$\\Leftrightarrow x(x + 2) + 3(x + 2) = 0$<br\/>$\\Leftrightarrow (x + 2)(x + 3) = 0$<br\/>$\\Leftrightarrow$ $\\left[\\begin{array}{l} x + 2 = 0\\\\ x + 3 = 0\\end{array} \\right.$<br\/>$\\Leftrightarrow$ $\\left[\\begin{array}{l} x = -2\\\\ x = -3\\end{array} \\right.$ (nh\u1eadn)<br\/>V\u1eady ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 t\u1eadp nghi\u1ec7m l\u00e0 $S = \\left\\{-3; -2; 2; 3\\right\\}$<br\/><span class='basic_pink'>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 $S = \\left\\{-3; -2; 2; 3\\right\\}$<\/span><\/span> ","column":2}]}],"id_ques":1191},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":10,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai27/lv3/img\/3.jpg' \/><\/center><br\/>T\u00ecm $m$ \u0111\u1ec3 ph\u01b0\u01a1ng tr\u00ecnh $|3-4x| + 2 = 5m + 12$ c\u00f3 nghi\u1ec7m duy nh\u1ea5t","select":[" A. $m = 2$"," B. $m = 3$","C. $m = -2$","D. $m = -3$"],"hint":"","explain":"<span class='basic_left'><span class='basic_green'>Ph\u01b0\u01a1ng ph\u00e1p gi\u1ea3i:<\/span><br\/>Cho ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 d\u1ea1ng $|P(x)| = k$ (trong \u0111\u00f3 $P(x)$ l\u00e0 bi\u1ec3u th\u1ee9c c\u1ee7a $x$, $k$ l\u00e0 m\u1ed9t s\u1ed1 cho tr\u01b0\u1edbc)<br\/>+ N\u1ebfu $k < 0$ th\u00ec ph\u01b0\u01a1ng tr\u00ecnh v\u00f4 nghi\u1ec7m<br\/>+ N\u1ebfu $k = 0$ th\u00ec ta c\u00f3 $|P(x)| = 0 \\Leftrightarrow P(x) = 0$ <br\/>+ N\u1ebfu $k > 0 $ th\u00ec ta c\u00f3 $|P(x)| = k \\Leftrightarrow \\left[\\begin{array}{l} P(x) = k \\\\ P(x) = -k\\end{array} \\right.$ <\/span> <br\/><span class='basic_left'><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Ta c\u00f3: <br\/>$|3-4x| + 2 = 5m + 12 \\Leftrightarrow |3 - 4x| = 5m + 10$<br\/>Ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 nghi\u1ec7m duy nh\u1ea5t khi v\u00e0 ch\u1ec9 khi $5m + 10 = 0 \\Leftrightarrow m = -2$ <br\/>V\u1eady \u0111i\u1ec1u ki\u1ec7n c\u1ee7a $m$ l\u00e0 $m = -2$ <br\/><span class='basic_pink'>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 C<\/span><\/span> <br\/><\/span><br\/> ","column":2}]}],"id_ques":1192},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":10,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai27/lv3/img\/5.jpg' \/><\/center><br\/>Gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh: $|x^2| - 5 + 4x = 0$","select":[" $S = \\left\\{0; 1\\right\\}$"," $S = \\left\\{1; 5\\right\\}$","$S = \\left\\{-3; -2\\right\\}$","$S = \\left\\{-5; 1\\right\\}$"],"hint":"B\u1ecf d\u1ea5u gi\u00e1 tr\u1ecb tuy\u1ec7t \u0111\u1ed1i r\u1ed3i gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh.","explain":"<span class='basic_left'>Ta c\u00f3: $x^2 \\geq 0 \\hspace{0,2cm} \\forall x \\Rightarrow |x^2| = x^2$<br\/>$|x^2| - 5 + 4x = 0$<br\/>$\\Leftrightarrow x^2 + 4x - 5 = 0$<br\/>$\\Leftrightarrow x^2 - 1 + 4x - 4 = 0$<br\/>$\\Leftrightarrow (x - 1)(x + 1) + 4(x - 1) = 0$<br\/>$\\Leftrightarrow (x - 1) (x + 1 + 4) = 0$<br\/>$\\Leftrightarrow (x - 1)(x + 5) = 0$<br\/>$\\Leftrightarrow$ $\\left[\\begin{array}{l} x - 1 = 0\\\\ x + 5 = 0\\end{array} \\right.$<br\/> $\\Leftrightarrow$ $\\left[\\begin{array}{l} x = 1\\\\ x = -5\\end{array} \\right.$<br\/> V\u1eady ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 t\u1eadp nghi\u1ec7m l\u00e0 $S = \\left\\{-5; 1\\right\\}$<br\/><span class='basic_pink'>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 $S = \\left\\{-5; 1\\right\\}$<\/span> ","column":2}]}],"id_ques":1193},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":10,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai27/lv3/img\/5.jpg' \/><\/center><br\/>Gi\u1ea3i b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh: $|x + 1| + |5 - x| > 8 + 2x$","select":[" $S = \\left\\{x \\mid x > -1\\right\\}$"," $S = \\left\\{x \\mid x > -7\\right\\}$","$S = \\left\\{x \\mid x < -7\\right\\}$","$S = \\left\\{x \\mid x < -1\\right\\}$"],"hint":"","explain":"<span class='basic_left'>+ V\u1edbi $x < -1$ ta c\u00f3: <br\/>$|x + 1| + |5 - x| > 8 + 2x \\Leftrightarrow -x - 1 + x - 5 > 8 + 2x \\Leftrightarrow 2x < -14 \\Leftrightarrow x < -7$ (nh\u1eadn)<br\/>+ V\u1edbi $-1 \\leq x < 5$ ta c\u00f3:<br\/>$|x + 1| + |5 - x| > 8 + 2x \\Leftrightarrow x + 1 + x - 5 > 8 + 2x \\Leftrightarrow 0 > 12$ (v\u00f4 l\u00ed)<br\/>V\u1edbi $x \\geq 5$ ta c\u00f3:<br\/>$|x + 1| + |5 - x| > 8 + 2x \\Leftrightarrow x + 1 + 5 - x > 8 + 2x \\Leftrightarrow 2x < -2 \\Leftrightarrow x < -1$ (lo\u1ea1i)<br\/>V\u1eady t\u1eadp nghi\u1ec7m c\u1ee7a b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 $S = \\left\\{x \\mid x < -7\\right\\}$<br\/><span class='basic_pink'>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 $S = \\left\\{x \\mid x < -7\\right\\}$<\/span><\/span> ","column":2}]}],"id_ques":1194},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":10,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai27/lv3/img\/6.jpg' \/><\/center><br\/>Gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh: $|x + 5| - |3x - 7| = 2x + 9$ (*)<br\/><b>T\u1eadp nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh l\u00e0:<\/b>","select":[" $S = \\left\\{-3; -4 \\right\\}$"," $S = \\varnothing$","$S = \\left\\{-5; \\dfrac{7}{3} \\right\\}$","$S = \\left\\{\\dfrac{3}{4}; \\dfrac{7}{3} \\right\\}$"],"hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>+ L\u1eadp b\u1ea3ng x\u00e9t \u0111i\u1ec1u ki\u1ec7n b\u1ecf d\u1ea5u gi\u00e1 tr\u1ecb tuy\u1ec7t \u0111\u1ed1i<br\/>+ C\u0103n c\u1ee9 b\u1ea3ng x\u00e9t d\u1ea5u chia t\u1eebng kho\u1ea3ng \u0111\u1ec3 gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh (ki\u1ec3m tra \u0111i\u1ec1u ki\u1ec7n t\u01b0\u01a1ng \u1ee9ng)<\/span> <br\/><span class='basic_left'><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Ta c\u00f3:<br\/> $|x + 5| =$ $ \\left\\{\\begin{array}{l} x + 5 \\hspace{0,2cm} \\text{n\u1ebfu}\\hspace{0,2cm} x \\geq -5\\\\ -x - 5 \\hspace{0,2cm} \\text{n\u1ebfu}\\hspace{0,2cm} x < -5\\end{array} \\right.$ v\u00e0 $|3x - 7| =$ $\\left\\{\\begin{array}{l} 3x - 7 \\hspace{0,2cm} \\text{n\u1ebfu}\\hspace{0,2cm} x \\geq \\dfrac{7}{3}\\\\ -3x + 7 \\hspace{0,2cm} \\text{n\u1ebfu}\\hspace{0,2cm} x < \\dfrac{7}{3}\\end{array} \\right.$<br\/>Ta c\u00f3 b\u1ea3ng sau:<br\/><center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai27/lv3/img\/D8C4B3_K101.png' \/><\/center><br\/>+ Tr\u01b0\u1eddng h\u1ee3p $1$: N\u1ebfu $x < -5$ th\u00ec ph\u01b0\u01a1ng tr\u00ecnh (*) tr\u1edf th\u00e0nh:<br\/>$-x - 5 - (-3x + 7) = 2x + 9$<br\/>$\\Leftrightarrow -x + 3x - 2x = 9 + 5 + 7$<br\/>$\\Leftrightarrow 0 = 21$ (v\u00f4 l\u00ed)<br\/>+ Tr\u01b0\u1eddng h\u1ee3p $2$: N\u1ebfu $-5 \\leq x < \\dfrac{7}{3}$ th\u00ec ph\u01b0\u01a1ng tr\u00ecnh (*) tr\u1edf th\u00e0nh:<br\/>$x + 5 - (-3x + 7) = 2x + 9$<br\/>$\\Leftrightarrow x + 5 + 3x - 7 = 2x + 9$<br\/>$\\Leftrightarrow 2x = 11$<br\/>$\\Leftrightarrow x = \\dfrac{11}{2}$ (lo\u1ea1i)<br\/>+ Tr\u01b0\u1eddng h\u1ee3p $3$: N\u1ebfu $x \\geq \\dfrac{7}{3}$ th\u00ec ph\u01b0\u01a1ng tr\u00ecnh (*) tr\u1edf th\u00e0nh:<br\/>$x + 5 - (3x - 7) = 2x + 9$<br\/>$\\Leftrightarrow x + 5 - 3x + 7 = 2x + 9$<br\/>$\\Leftrightarrow -4x = -3$<br\/>$\\Leftrightarrow x = \\dfrac{3}{4} $ (lo\u1ea1i)<br\/>V\u1eady t\u1eadp nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 $S = \\varnothing$<br\/><span class='basic_pink'>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 $S = \\varnothing$<\/span><\/span> <br\/><\/span><br\/> ","column":2}]}],"id_ques":1195},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":10,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai27/lv3/img\/7.jpg' \/><\/center><br\/>Gi\u1ea3i b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh: $|4x + 3| \\geq |3x - 5|$<br\/><b> T\u1eadp nghi\u1ec7m c\u1ee7a b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh l\u00e0:<\/b> ","select":[" A. $x \\geq \\dfrac{2}{7}$ ho\u1eb7c $x \\leq 8 $"," B. $x \\geq \\dfrac{2}{7}$ ho\u1eb7c $x \\leq -8 $","C. $x \\leq \\dfrac{2}{7}$ ho\u1eb7c $x \\leq -8 $","D. $x \\geq \\dfrac{2}{7}$ ho\u1eb7c $x \\geq -8 $"],"hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>$|A| \\geq |B| \\Leftrightarrow A^2 \\geq B^2 \\Leftrightarrow A^2 - B^2 \\geq 0 \\Leftrightarrow (A-B)(A +B) \\geq 0$<\/span> <br\/><span class='basic_left'><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Ta c\u00f3:<br\/>$|4x + 3| \\geq |3x - 5|$<br\/>$\\Leftrightarrow (4x + 3)^2 \\geq (3x - 5)^2$<br\/>$\\Leftrightarrow (4x + 3)^2 - (3x - 5)^2 \\geq 0$<br\/>$\\Leftrightarrow (4x + 3 + 3x - 5)(4x + 3 - 3x + 5) \\geq 0$<br\/>$\\Leftrightarrow (7x - 2)(x + 8) \\geq 0$<br\/><b> Tr\u01b0\u1eddng h\u1ee3p $1$:<\/b><br\/>$\\left\\{\\begin{array}{l} 7x - 2 \\geq 0\\\\ x + 8 \\geq 0 \\end{array} \\right.$ $\\Leftrightarrow$ $\\left\\{\\begin{array}{l} x \\geq \\dfrac{2}{7}\\\\ x \\geq -8 \\end{array} \\right.$ $\\Leftrightarrow$ $x \\geq \\dfrac{2}{7}$<br\/><b>Tr\u01b0\u1eddng h\u1ee3p $2$:<\/b><br\/>$\\left\\{\\begin{array}{l} 7x - 2 \\leq 0\\\\ x + 8 \\leq 0 \\end{array} \\right.$ $\\Leftrightarrow$ $\\left\\{\\begin{array}{l} x \\leq \\dfrac{2}{7}\\\\ x \\leq -8 \\end{array} \\right.$ $\\Leftrightarrow$ $x \\leq -8 $<br\/>V\u1eady nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 $x \\geq \\dfrac{2}{7}$ ho\u1eb7c $x \\leq -8 $<br\/><span class='basic_pink'>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 B<\/span> <\/span> <br\/><\/span><br\/> ","column":2}]}],"id_ques":1196},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":10,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai27/lv3/img\/7.jpg' \/><\/center><br\/>Gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh: $||x + 2| - 3| = 7$<br\/><b> T\u1eadp nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh l\u00e0:<\/b> ","select":[" $S = \\left\\{8 \\right\\}$"," $S = \\left\\{-12 \\right\\}$","$S = \\left\\{-8; 12 \\right\\}$","$S = \\left\\{-12; 8 \\right\\}$"],"hint":"B\u1ecf t\u1eebng gi\u00e1 tr\u1ecb tuy\u1ec7t \u0111\u1ed1i r\u1ed3i gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh.","explain":"<span class='basic_left'>$|x + 2| - 3| = 7$ $\\Leftrightarrow$ $\\left[\\begin{array}{l} |x + 2| - 3 = 7\\\\ |x + 2| - 3 = -7 \\end{array} \\right.$ $\\Leftrightarrow$ $\\left[\\begin{array}{l} |x + 2| = 10 \\hspace{0,2cm} (1) \\\\ |x + 2| = -4 \\text{(lo\u1ea1i)} \\end{array} \\right.$<br\/> $(1) \\Leftrightarrow \\left[\\begin{array}{l} x + 2 = 10 \\text{(n\u1ebfu)} \\hspace{0,2cm} x \\geq -2 \\\\ x + 2 = -10 \\text{n\u1ebfu} \\hspace{0,2cm} x < -2 \\end{array} \\right.$ $\\Leftrightarrow \\left[\\begin{array}{l} x = 8 \\text{(nh\u1eadn)} \\\\ x = -12 \\text{(nh\u1eadn)} \\end{array} \\right.$<br\/>V\u1eady t\u1eadp nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 $S = \\left\\{-12; 8 \\right\\}$<br\/><span class='basic_pink'>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 $S = \\left\\{-12; 8 \\right\\}$<\/span><\/span> ","column":2}]}],"id_ques":1197},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":10,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai27/lv3/img\/4.jpg' \/><\/center><br\/>Gi\u1ea3i b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh: $|2x - 6| \\leq |3x + 4|$<br\/><b> T\u1eadp nghi\u1ec7m c\u1ee7a b\u1ea5t ph\u01b0\u01a1ng tr\u00ecnh l\u00e0:<\/b> ","select":[" A. $x \\geq \\dfrac{2}{5}$ ho\u1eb7c $x \\leq -10 $"," B. $x \\geq \\dfrac{-2}{5}$ ho\u1eb7c $x \\leq 10 $","C. $x \\leq \\dfrac{2}{5}$ ho\u1eb7c $x \\leq -10 $","D. $x \\geq \\dfrac{2}{5}$ ho\u1eb7c $x \\geq -10$"],"hint":"","explain":"<span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span><br\/>$|A| \\leq |B| \\Leftrightarrow A^2 \\leq B^2 \\Leftrightarrow A^2 - B^2 \\leq 0 \\Leftrightarrow (A-B)(A +B) \\leq 0$<\/span> <br\/><span class='basic_left'><span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/>Ta c\u00f3:<br\/>$|2x - 6| \\leq |3x + 4|$<br\/>$\\Leftrightarrow (2x - 6)^2 \\leq (3x + 4)^2$<br\/>$\\Leftrightarrow (2x - 6)^2 - (3x + 4)^2 \\leq 0$<br\/>$\\Leftrightarrow (2x - 6 + 3x + 4)(2x - 6 - 3x - 4) \\leq 0$<br\/>$\\Leftrightarrow (5x - 2)(-x - 10) \\leq 0$<br\/><b> Tr\u01b0\u1eddng h\u1ee3p $1$:<\/b><br\/>$\\left\\{\\begin{array}{l} 5x - 2 \\leq 0\\\\ -x - 10 \\geq 0 \\end{array} \\right.$ $\\Leftrightarrow$ $\\left\\{\\begin{array}{l} x \\leq \\dfrac{2}{5}\\\\ x \\leq -10 \\end{array} \\right.$ $\\Leftrightarrow$ $x \\leq -10$<br\/><b>Tr\u01b0\u1eddng h\u1ee3p $2$:<\/b><br\/>$\\left\\{\\begin{array}{l} 5x - 2 \\geq 0\\\\ -x - 10 \\leq 0 \\end{array} \\right.$ $\\Leftrightarrow$ $\\left\\{\\begin{array}{l} x \\geq \\dfrac{2}{5}\\\\ x \\geq -10 \\end{array} \\right.$ $\\Leftrightarrow$ $x \\geq \\dfrac{2}{5} $<br\/>V\u1eady nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 $x \\geq \\dfrac{2}{5}$ ho\u1eb7c $x \\leq -10 $<br\/><span class='basic_pink'>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 A<\/span> <\/span> <br\/><\/span><br\/> ","column":2}]}],"id_ques":1198},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":10,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai27/lv3/img\/4.jpg' \/><\/center><br\/>Gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh: $\\left| x + \\dfrac{1}{1.3}\\right| + \\left| x + \\dfrac{1}{3.5}\\right| + ... + \\left| x + \\dfrac{1}{97.99}\\right| = 50x$ ","select":[" A. $x = \\dfrac{-49}{99}$"," B. $x = \\dfrac{-50}{99}$","C. $x = \\dfrac{49}{99}$","D. $x = \\dfrac{50}{99}$"],"hint":"","explain":"<span class='basic_left'>Nh\u1eadn th\u1ea5y v\u1ebf tr\u00e1i kh\u00f4ng \u00e2m v\u1edbi m\u1ecdi $x$ n\u00ean \u0111i\u1ec1u ki\u1ec7n c\u1ea7n \u0111\u1ec3 $x$ l\u00e0 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 v\u1ebf ph\u1ea3i kh\u00f4ng \u00e2m, t\u1ee9c l\u00e0: $50x \\geq 0 \\Leftrightarrow x \\geq 0$<br\/>Khi \u0111\u00f3 c\u00e1c bi\u1ec3u th\u1ee9c trong t\u1ea5t c\u1ea3 c\u00e1c d\u1ea5u gi\u00e1 tr\u1ecb tuy\u1ec7t \u0111\u1ed1i \u1edf v\u1ebf tr\u00e1i \u0111\u1ec1u d\u01b0\u01a1ng.<br\/>V\u00ec v\u1eady ph\u01b0\u01a1ng tr\u00ecnh tr\u1edf th\u00e0nh:<br\/>$\\left( x + \\dfrac{1}{1.3}\\right) + \\left( x + \\dfrac{1}{3.5}\\right) + ... + \\left( x + \\dfrac{1}{97.99}\\right) = 50x$<br\/> $\\Leftrightarrow \\left( \\dfrac{1}{1.3} + \\dfrac{1}{3.5} + ... + \\dfrac{1}{97.99}\\right) + 49x = 50x$<br\/>$\\Leftrightarrow x = \\dfrac{1}{1.3} + \\dfrac{1}{3.5} + ... + \\dfrac{1}{97.99}$<br\/>$\\Leftrightarrow 2x = \\dfrac{2}{1.3} + \\dfrac{2}{3.5} + ... + \\dfrac{2}{97.99}$<br\/>$\\Leftrightarrow 2x = 1- \\dfrac{1}{3} + \\dfrac{1}{3} - \\dfrac{1}{5} + \\dfrac{1}{5 } - ... + \\dfrac{1}{97} - \\dfrac{1}{99}$<br\/>$\\Leftrightarrow 2x = 1 - \\dfrac{1}{99}$<br\/>$\\Leftrightarrow 2x = \\dfrac{98}{99}$<br\/>$\\Leftrightarrow x = \\dfrac{49}{99}$ (th\u1ecfa m\u00e3n \u0111i\u1ec1u ki\u1ec7n $x \\geq 0$)<br\/>V\u1eady ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 nghi\u1ec7m duy nh\u1ea5t l\u00e0 $x = \\dfrac{49}{99}$<br\/><span class='basic_pink'>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 C<\/span><\/span> ","column":2}]}],"id_ques":1199},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":10,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop8/toan/daiso/bai27/lv3/img\/4.jpg' \/><\/center><br\/>Gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh: $\\left| x + \\dfrac{1}{2.3}\\right| + \\left| x + \\dfrac{1}{3.4}\\right| + ... + \\left| x + \\dfrac{1}{98.99}\\right| = 98x$ ","select":[" A. $x = \\dfrac{97}{198}$"," B. $x = \\dfrac{98}{198}$","C. $x = \\dfrac{99}{198}$","D. $x = \\dfrac{100}{198}$"],"hint":"","explain":"<span class='basic_left'>Nh\u1eadn th\u1ea5y v\u1ebf tr\u00e1i kh\u00f4ng \u00e2m v\u1edbi m\u1ecdi $x$ n\u00ean \u0111i\u1ec1u ki\u1ec7n c\u1ea7n \u0111\u1ec3 $x$ l\u00e0 nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh l\u00e0 v\u1ebf ph\u1ea3i kh\u00f4ng \u00e2m, t\u1ee9c l\u00e0: $98x \\geq 0 \\Leftrightarrow x \\geq 0$<br\/>Khi \u0111\u00f3 c\u00e1c bi\u1ec3u th\u1ee9c trong t\u1ea5t c\u1ea3 c\u00e1c d\u1ea5u gi\u00e1 tr\u1ecb tuy\u1ec7t \u0111\u1ed1i \u1edf v\u1ebf tr\u00e1i \u0111\u1ec1u d\u01b0\u01a1ng.<br\/>V\u00ec v\u1eady ph\u01b0\u01a1ng tr\u00ecnh tr\u1edf th\u00e0nh:<br\/>$\\left( x + \\dfrac{1}{2.3}\\right) + \\left( x + \\dfrac{1}{3.4}\\right) + ... + \\left( x + \\dfrac{1}{98.99}\\right) = 98x$<br\/> $\\Leftrightarrow \\left( \\dfrac{1}{2.3} + \\dfrac{1}{3.4} + ... + \\dfrac{1}{98.99}\\right) + 97x = 98x$<br\/>$\\Leftrightarrow x = \\dfrac{1}{2.3} + \\dfrac{1}{3.4} + ... + \\dfrac{1}{98.99}$<br\/>$\\Leftrightarrow x = \\dfrac{1}{2}- \\dfrac{1}{3} + \\dfrac{1}{3} - \\dfrac{1}{4} + \\dfrac{1}{4 } - ... + \\dfrac{1}{98} - \\dfrac{1}{99}$<br\/>$\\Leftrightarrow x = \\dfrac{1}{2} - \\dfrac{1}{99}$<br\/>$\\Leftrightarrow x = \\dfrac{97}{198}$ (th\u1ecfa m\u00e3n \u0111i\u1ec1u ki\u1ec7n $x \\geq 0$)<br\/>V\u1eady ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 nghi\u1ec7m duy nh\u1ea5t l\u00e0 $x = \\dfrac{97}{198}$<br\/><span class='basic_pink'>\u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 A<\/span><\/span> ","column":2}]}],"id_ques":1200}],"lesson":{"save":0,"level":3}}