What is the answer to |x+4|=|2x-7| ?

The answer to |x+4|=|2x-7| is x=1\lor x=11

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|x+4|=|2x-7|

∣ x + 4 ∣ = ∣ 2 x - 7 ∣

x = 1 or x = 11

Solution steps

∣ x + 4 ∣ = ∣ 2 x - 7 ∣

Find positive and negative intervals

x < - 4, - 4 \leq x < \frac{7}{2}, x \geq \frac{7}{2}

Solve the inequality for each interval

No Solution or x = 1 or x = 11

x = 1 or x = 11

4 x^{4} + 4 x^{3} + 5 x^{2} + 4 x + 1

t^{2} + 6 t + 8

1 - ln (x) \geq 0

\frac{1}{7} \cdot \frac{7}{11}

\frac{1}{3} (3)