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

1 Answer
A. S. Adikesavan
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 >+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]}

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