Đáp án:
e) \(x = \dfrac{4}{7}\)
Giải thích các bước giải:
\(\begin{array}{l}
a)\left| {x + 2} \right| = \dfrac{8}{5}\\
\to \left[ \begin{array}{l}
x + 2 = \dfrac{8}{5}\\
x + 2 = - \dfrac{8}{5}
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = - \dfrac{2}{5}\\
x = - 6
\end{array} \right.\\
b)\left| {8 - 3x} \right| = 1\\
\to \left[ \begin{array}{l}
8 - 3x = 1\left( {DK:\dfrac{8}{3} \ge x} \right)\\
8 - 3x = - 1\left( {DK:\dfrac{8}{3} < x} \right)
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = \dfrac{7}{3}\\
x = 3
\end{array} \right.\left( {TM} \right)\\
c)\left| {3x + 1} \right| = 5\\
\to \left[ \begin{array}{l}
3x + 1 = 5\\
3x + 1 = - 5
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = \dfrac{4}{3}\\
x = - 2
\end{array} \right.\\
d)\left| {x + 4} \right| = 2x - 6\\
\to \left[ \begin{array}{l}
x + 4 = 2x - 6\\
x + 4 = - 2x + 6
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = 10\\
3x = 2
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = 10\\
x = \dfrac{2}{3}
\end{array} \right.\\
e)\left| {2x + 5} \right| = 8\\
\to \left[ \begin{array}{l}
2x + 5 = 8\\
2x + 5 = - 8
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = \dfrac{3}{2}\\
x = - \dfrac{{13}}{2}
\end{array} \right.\\
f)\left| {x + 2} \right| = 6 - 2x\\
\to \left[ \begin{array}{l}
x + 2 = 6 - 2x\left( {DK:x \ge - 2} \right)\\
x + 2 = - 6 + 2x\left( {DK:x < - 2} \right)
\end{array} \right.\\
\to \left[ \begin{array}{l}
3x = 4\\
x = 8\left( l \right)
\end{array} \right.\\
\to x = \dfrac{4}{3}\\
g)\left| {2x - 3} \right| = 5x - 1\\
\to \left[ \begin{array}{l}
2x - 3 = 5x - 1\left( {DK:x \ge \dfrac{3}{2}} \right)\\
2x - 3 = - 5x + 1\left( {DK:x < \dfrac{3}{2}} \right)
\end{array} \right.\\
\to \left[ \begin{array}{l}
3x = - 2\\
7x = 4
\end{array} \right.\\
\to \left[ \begin{array}{l}
x = - \dfrac{2}{3}\left( l \right)\\
x = \dfrac{4}{7}
\end{array} \right.
\end{array}\)
