# How do you solve abs(5x+4) =abs(2x+5)?

Apr 3, 2015

Answers: $x = \frac{1}{3}$ , $x = - \frac{9}{7}$

$| 5 x + 4 | = | 2 x + 5 |$

Squaring both sides of the equation you get,

${\left(5 x + 4\right)}^{2} = {\left(2 x + 5\right)}^{2}$

$\implies {\left(5 x + 4\right)}^{2} - {\left(2 x + 5\right)}^{2} = 0$

Using the idea that, ${a}^{2} - {b}^{2} = \left(a - b\right) \left(a + b\right)$ ,

=> (5x + 4 -(2x + 5))(5x + 4 + 2x + 5)) = 0

$\implies \left(3 x - 1\right) \left(7 x + 9\right) = 0$

$\implies 3 x - 1 = 0 \implies x = \frac{1}{3}$

$7 x + 9 = 0 \implies x = - \frac{9}{7}$