Đáp án:
$a.$ \(\left[ \begin{array}{l}x=\frac{1}{2}\\x=-\frac{21}{10}\end{array} \right.\)
$b.$ \(\left[ \begin{array}{l}x=\frac{1}{2}\\x=-\frac{1}{2}\end{array} \right.\)
$c.$ \(\left[ \begin{array}{l}x=\frac{16}{63}\\x=-\frac{16}{63}\end{array} \right.\)
$d.$ \(\left[ \begin{array}{l}x=1\\x=2\end{array} \right.\)
Giải thích các bước giải:
$a. | 2x - \frac{8}{-5} | - \frac{8}{5} = 1$
⇔ $| 2x + \frac{8}{5} | = 1 + \frac{8}{5}$
⇔ $| 2x + \frac{8}{5} | = \frac{13}{5}$
⇔ \(\left[ \begin{array}{l}2x+\frac{8}{5}=\frac{13}{5}\\2x+\frac{8}{5}=-\frac{13}{5}\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}2x=\frac{13}{5}-\frac{8}{5}\\x=-\frac{13}{5}-\frac{8}{5}\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}2x=1\\x=-\frac{21}{5}\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x=\frac{1}{2}\\x=-\frac{21}{10}\end{array} \right.\)
$b. 4 - | 2x | = 3$
⇔ $| 2x | = 4 - 3$
⇔ $| 2x | = 1$
⇔ \(\left[ \begin{array}{l}2x=1\\2x=-1\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x=\frac{1}{2}\\x=-\frac{1}{2}\end{array} \right.\)
$c. - \frac{1}{3} + | 3x | = \frac{3}{7}$
⇔ $| 3x | = \frac{3}{7} + \frac{1}{3}$
⇔ $| 3x | = \frac{9}{21} + \frac{7}{21}$
⇔ $| 3x | = \frac{16}{21}$
⇔ \(\left[ \begin{array}{l}3x=\frac{16}{21}\\3x=-\frac{16}{21}\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x=\frac{16}{63}\\x=-\frac{16}{63}\end{array} \right.\)
$d. | 1\frac{1}{2} - x | = \frac{1}{2}$
⇔ $| 1 + \frac{1}{2} - x | = \frac{1}{2}$
⇔ \(\left[ \begin{array}{l}1+\frac{1}{2}-x=\frac{1}{2}\\1+\frac{1}{2}-x=-\frac{1}{2}\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x=1+\frac{1}{2}-\frac{1}{2}\\x=1+\frac{1}{2}+\frac{1}{2}\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x=1\\x=1+\frac{2}{2}\end{array} \right.\)
⇔ \(\left[ \begin{array}{l}x=1\\x=2\end{array} \right.\)
