# How do you solve |-4x-3| = |-7x+7|?

Dec 3, 2017

${x}_{1} = \frac{4}{11}$ and ${x}_{2} = \frac{10}{3}$

#### Explanation:

$\left\mid - 4 x - 3 \right\mid = \left\mid - 7 x + 7 \right\mid$

${\left(- 4 x - 3\right)}^{2} = {\left(- 7 x + 7\right)}^{2}$

$16 {x}^{2} + 24 x + 9 = 49 {x}^{2} - 98 x + 49$

$33 {x}^{2} - 122 x + 40$

$33 {x}^{2} - 110 x - 12 x + 40 = 0$

$11 x \cdot \left(3 x - 10\right) - 4 \cdot \left(3 x - 10\right) = 0$

$\left(11 x - 4\right) \cdot \left(3 x - 10\right) = 0$

Hence ${x}_{1} = \frac{4}{11}$ and ${x}_{2} = \frac{10}{3}$