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

Jan 16, 2017

1/5 and 7. See the x-intercepts, in the illustrative Socratic graph.

#### Explanation:

The x-intercepts 1/5 and 7 in the graph are the solutions.

Algebraic proof:

If $x > + \frac{4}{3} , 3 x - 4 = 2 x + 3$, giving x = 7.

If $- \frac{3}{2} \le x \le \frac{4}{3} , 4 - 3 x = 2 x + 3$, giving $x = \frac{1}{5}$.

If $x \le - \frac{3}{2} , 4 - 3 x = - \left(2 x + 3\right)$, repeating x = 7#.

graph{|3x-4|-|2x+3| [0, 7, -10.04, 10.04]}