#### Answer

$[-\frac{7}{4}, \frac{9}{4}]$

#### Work Step by Step

1. In order for the equation to be true, the equation between the absolute value brackets must be between -8 and 8. Redefine the equation to get rid of the absolute value brackets:
$|4x-1| \leq 8$
$-8 \leq 4x-1 \leq 8$
2. Solve each side of the equation
$-8 \leq 4x-1$
$-7 \leq 4x$ (Add 1 to each side)
$-\frac{7}{4} \leq x$ (Divide each side by 4)
$4x-1 \leq 8$
$4x \leq 9$ (Add 1 to each side)
$x \leq \frac{9}{4}$ (Divide each side by 4)
3. Since the original equation is said to be less than or equal ($\leq$) to 8, place your final answer in square brackets
$[-\frac{7}{4}, \frac{9}{4}]$