Question

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

Answer 1

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 >+4/3, 3x-4=2x+3`, giving x = 7.

If `-3/2<=x<=4/3, 4-3x=2x+3`, giving `x =1/5`.

If `x<=-3/2, 4-3x=-(2x+3)`, repeating x = 7#.

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