1. Tìm x, biết:
a) $2|2x-3| = \frac{1}{2}$
b) $7,5 - 3|5-2x| = -4,5$
c) $\left |x+\frac{4}{15} \right |-|-3,75| = -|-2,15|$
2. Tìm x, biết:
a) $6,5 - \frac{9}{4}:\left | x+\frac{1}{3} \right |=2$
b) $\frac{11}{4}+\frac{3}{2}:\left | 4x-\frac{1}{5} \right |=\frac{7}{2}$
Bài Làm:
1.
a) $2|2x-3| = \frac{1}{2}$
$\Leftrightarrow 2(2x-3)= \frac{1}{2}$
$\Leftrightarrow 4x-6= \frac{1}{2}$ hoặc $4x-6= -\frac{1}{2}$
$\Leftrightarrow x=\frac{13}{8}$ hoặc $x=\frac{11}{8}$
Vậy $x=\frac{13}{8}$ hoặc $x=\frac{11}{8}$
b) $7,5 - 3|5-2x| = -4,5$
$\Leftrightarrow 3|5-2x| = 12$
$\Leftrightarrow |5-2x| = 4$
$\Leftrightarrow 5-2x = 4$ hoặc $5 - 2x = -4$
$\Leftrightarrow x=\frac{1}{2}$ hoặc $x = \frac{9}{2}$
c) $\left |x+\frac{4}{15} \right |-|-3,75| = -|-2,15|$
$\Leftrightarrow \left |x+\frac{4}{15} \right |-3,75 = -2,15$
$\Leftrightarrow \left |x+\frac{4}{15} \right |=\frac{8}{5}$
$\Leftrightarrow x+\frac{4}{15} = \frac{8}{5}$ hoặc $x+\frac{4}{15} = -\frac{8}{5}$
$\Leftrightarrow x=\frac{4}{3}$ hoặc $x=\frac{-28}{15}$
2.
a) $6,5 - \frac{9}{4}:\left | x+\frac{1}{3} \right |=2$
$\Leftrightarrow \frac{9}{4}:\left | x+\frac{1}{3} \right |=\frac{9}{2}$
$\left | x+\frac{1}{3} \right | = \frac{1}{2}$
$\Leftrightarrow x+\frac{1}{3}=\frac{1}{2}$ hoặc $x+\frac{1}{3}=-\frac{1}{2}$
$\Leftrightarrow x=\frac{1}{6}$ hoặc $x=\frac{-5}{6}$
Vậy $x=\frac{1}{6}$ hoặc $x=\frac{-5}{6}$
b) $\frac{11}{4}+\frac{3}{2}:\left | 4x-\frac{1}{5} \right |=\frac{7}{2}$
$\Leftrightarrow \frac{3}{2}:\left | 4x-\frac{1}{5} \right |=\frac{3}{4}$
$\Leftrightarrow \left | 4x-\frac{1}{5} \right |=2$
$\Leftrightarrow 4x-\frac{1}{5}=2$ hoặc $4x-\frac{1}{5}=-2$
$\Leftrightarrow x=\frac{11}{20}$ hoặc $x=\frac{-9}{20}$
Vậy $x=\frac{11}{20}$ hoặc $x=\frac{-9}{20}$