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

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Answer 1 · 2017-01-16T01:54:58

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

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

Algebraic proof:

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

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

If $x \leq - \frac{3}{2}, 4 - 3 x = - (2 x + 3)$ $x<=-3/2, 4-3x=-(2x+3)$ , repeating x = 7#.

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

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