# How do you solve ｜x+1｜=｜3x-2｜?

Feb 1, 2017

Solution $x = \frac{1}{4} \mathmr{and} x = \frac{3}{2}$

#### Explanation:

$| x + 1 | = | 3 x - 2 |$ squaring both sides we get , ${\left(x + 1\right)}^{2} = {\left(3 x - 2\right)}^{2} \mathmr{and} {x}^{2} + 2 x + 1 = 9 {x}^{2} - 12 x + 4 \mathmr{and} 8 {x}^{2} - 14 x + 3 = 0 \mathmr{and} 8 {x}^{2} - 12 x - 2 x + 3 = 0 \mathmr{and} 4 x \left(2 x - 3\right) - 1 \left(2 x - 3\right) = 0 \mathmr{and} \left(4 x - 1\right) \left(2 x - 3\right) = 0 \therefore$Either $\left(4 x - 1\right) = 0 \therefore x = \frac{1}{4}$ Or $\left(2 x - 3\right) = 0 \therefore x = \frac{3}{2}$

Solution $x = \frac{1}{4} \mathmr{and} x = \frac{3}{2}$[Ans]