giải phương trình :a|3x|=x+7
b |-4x|=x+2
c |5x|=x+7
d |2-x|=2-3x
e |2x-3|=5x-6
f |x-9|=2x+5
g 2x-|6x-7|=-x+8
h 9-|-5x|+2x=0
Đáp án:
$\begin{array}{l}
a)Dk:x + 7 \ge 0\\
\Rightarrow x \ge – 7\\
\left| {3x} \right| = x + 7\\
\Rightarrow \left[ \begin{array}{l}
3x = x + 7\\
3x = – x – 7
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
x = \frac{7}{2}\left( {tm} \right)\\
x = \frac{{ – 7}}{4}\left( {tm} \right)
\end{array} \right.\\
b)\left| { – 4x} \right| = x + 2\left( {dk:x \ge – 2} \right)\\
\Rightarrow \left[ \begin{array}{l}
– 4x = x + 2\\
4x = x + 2
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
x = – \frac{2}{5}\left( {tm} \right)\\
x = \frac{2}{3}\left( {tm} \right)
\end{array} \right.\\
c)\left| {5x} \right| = x + 7\left( {dk:x \ge – 7} \right)\\
\Rightarrow \left[ \begin{array}{l}
5x = x + 7\\
5x = – x – 7
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
x = \frac{7}{4}\left( {tm} \right)\\
x = – \frac{7}{6}\left( {tm} \right)
\end{array} \right.\\
d)\left| {2 – x} \right| = 2 – 3x\left( {dk:x \le \frac{2}{3}} \right)\\
\Rightarrow \left[ \begin{array}{l}
2 – x = 2 – 3x\\
2 – x = 3x – 2
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
x = 0\left( {tm} \right)\\
x = 1\left( {ktm} \right)
\end{array} \right.\\
Vậy\,x = 0\\
e)\left| {2x – 3} \right| = 5x – 6\left( {dk:x \ge \frac{6}{5}} \right)\\
\Rightarrow \left[ \begin{array}{l}
2x – 3 = 5x – 6\\
2x – 3 = 6 – 5x
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
x = 1\left( {ktm} \right)\\
x = \frac{9}{7}\left( {tm} \right)
\end{array} \right.\\
Vậy\,x = \frac{9}{7}\\
f)\left| {x – 9} \right| = 2x + 5\left( {dk:x \ge – \frac{5}{2}} \right)\\
\Rightarrow \left[ \begin{array}{l}
x – 9 = 2x + 5\\
x – 9 = – 2x – 5
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
x = – 14\left( {ktm} \right)\\
x = \frac{4}{3}\left( {tm} \right)
\end{array} \right.\\
Vậy\,x = \frac{4}{3}\\
g)2x – \left| {6x – 7} \right| = – x + 8\\
\Rightarrow \left| {6x – 7} \right| = 3x – 8\left( {dk:x \ge \frac{8}{3}} \right)\\
\Rightarrow \left[ \begin{array}{l}
6x – 7 = 3x – 8\\
6x – 7 = 8 – 3x
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
x = – \frac{1}{3}\left( {ktm} \right)\\
x = \frac{5}{3}\left( {ktm} \right)
\end{array} \right.\\
\Rightarrow Pt\,vô\,nghiệm\\
h)9 – \left| { – 5x} \right| + 2x = 0\\
\Rightarrow \left| { – 5x} \right| = 9 + 2x\left( {dk:x \ge – \frac{9}{2}} \right)\\
\Rightarrow \left[ \begin{array}{l}
– 5x = 9 + 2x\\
5x = 9 + 2x
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
x = \frac{{ – 9}}{7}\left( {tm} \right)\\
x = 1\left( {tm} \right)
\end{array} \right.
\end{array}$