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

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

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

∣ 2 x - 7 ∣ = ∣ x + 4 ∣

x = 1 or x = 11

Solution steps

∣ 2 x - 7 ∣ = ∣ x + 4 ∣

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 - 2 ∣ = ∣ x + 7 ∣

\frac{x - 2}{3} - 0 (3) = \frac{1}{3}

2 ∣ x ∣ + ∣ 2 x + 3 ∣ = 7

2 ∣ x - 1 ∣ = 2 x - 7

∣ x - 3 ∣ = x^{2} - 5 x + 6