# How do you solve 3abs(2x-6)= 4x-7?

Aug 14, 2015

$x = \frac{5}{2} \text{ or } x = \frac{11}{2}$

#### Explanation:

Method 1:
$3 | 2 x - 6 | = 4 x - 7$
Take the square on both sides to remove the modulus sign
$9 {\left(2 x - 6\right)}^{2} = {\left(4 x - 7\right)}^{2}$
$9 \left(4 {x}^{2} - 24 x + 36\right) = 16 {x}^{2} - 56 x + 49$
$4 {x}^{2} - 32 x + 55 = 0$
$\left(2 x - 5\right) \left(2 x - 11\right) = 0$
$x = \frac{5}{2} \text{ or } x = \frac{11}{2}$

Check that both solutions are correct since we squared the initial equation.

Method 2:
$3 | 2 x - 6 | = 4 x - 7$
$3 \left(2 x - 6\right) = 4 x - 7 \text{ or } - 3 \left(2 x - 6\right) = 4 x - 7$
$2 x = 11 \text{ or } 10 x = 25$
$x = \frac{11}{2} \text{ or } x = \frac{5}{2}$

graph{(3|2x-6|-y)(4x-7-y) = 0 [-5, 10, -40, 40]}