Answer
Solution set = $\displaystyle \{\frac{1}{3}, \frac{7}{3}\}$
Work Step by Step
$ 4\displaystyle \left| 1-\frac{3}{4}x\right|+7=10\qquad$ ... subtract $7$
... isolate the absolute value bracket
$ 4\displaystyle \left| 1-\frac{3}{4}x\right|=3\qquad$ ... divide with $4$
$\displaystyle \left| 1-\frac{3}{4}x\right|=\frac{3}{4}\qquad$ ... remove absolute value
$\left.\begin{array}{lllll}
1-\frac{3}{4}x=\frac{3}{4} & /\times 4 & or & 1-\frac{3}{4}x=-\frac{3}{4} & /\times 4\\
4-3x=3 & /-4 & & 4-3x=-3 & /-4\\
-3x=-1 & /\div(-3) & & -3x=-7 & /\div(-3)\\
x=1/3 & & & x=7/3 &
\end{array}\right.$
Solution set = $\displaystyle \{\frac{1}{3}, \frac{7}{3}\}$
