3. Tìm x biết:
a) |5x - 4| = |x + 2|
b) |2x - 3| - |3x + 2| = 0
c) $\left | \frac{3}{2}x+\frac{1}{2} \right |=|4x-1|$
d) $\left | \frac{5}{4}x-\frac{7}{2} \right |-\left | \frac{5}{8}x+\frac{3}{5} \right |$
Bài Làm:
a) |5x - 4| = |x + 2|
$\Leftrightarrow 5x-4=x+2$ hoặc $5x-4=-(x+2)$
$\Leftrightarrow x=\frac{3}{2}$ hoặc $x=\frac{1}{3}$
Vậy $x=\frac{3}{2}$ hoặc $x=\frac{1}{3}$
b) |2x - 3| - |3x + 2| = 0
$\Leftrightarrow |2x - 3| = |3x + 2|$
$\Leftrightarrow 2x - 3=3x+2$ hoặc $2x - 3=-(3x+2)$
$\Leftrightarrow x=-5$ hoặc $x=\frac{1}{5}$
Vậy $x=-5$ hoặc $x=\frac{1}{5}$
c) $\left | \frac{3}{2}x+\frac{1}{2} \right |=|4x-1|$
$\Leftrightarrow \frac{3}{2}x+\frac{1}{2}=4x-1$ hoặc $\frac{3}{2}x+\frac{1}{2}=-(4x-1)$
$\Leftrightarrow x=\frac{3}{5}$ hoặc $x=\frac{1}{11}$
Vậy $x=\frac{3}{5}$ hoặc $x=\frac{1}{11}$
d) $\left | \frac{5}{4}x-\frac{7}{2} \right |-\left | \frac{5}{8}x+\frac{3}{5} \right |$
$\Leftrightarrow \left | \frac{5}{4}x-\frac{7}{2} \right |=\left | \frac{5}{8}x+\frac{3}{5} \right |$
$\Leftrightarrow \frac{5}{4}x-\frac{7}{2} = \frac{5}{8}x+\frac{3}{5}$ hoặc $\frac{5}{4}x-\frac{7}{2} = -\left (\frac{5}{8}x+\frac{3}{5} \right )$
$\Leftrightarrow x=\frac{-55}{4}$ hoặc $x=\frac{-25}{164}$
Vậy $x=\frac{-55}{4}$ hoặc $x=\frac{-25}{164}$