What is the answer to |x+8|=|2x+1| ?

The answer to |x+8|=|2x+1| is x=-3\lor x=7

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|x+8|=|2x+1|

∣ x + 8 ∣ = ∣ 2 x + 1 ∣

x = - 3 or x = 7

Solution steps

∣ x + 8 ∣ = ∣ 2 x + 1 ∣

Find positive and negative intervals

x < - 8, - 8 \leq x < - \frac{1}{2}, x \geq - \frac{1}{2}

Solve the inequality for each interval

No Solution or x = - 3 or x = 7

x = - 3 or x = 7

x, ∣ - 3 x + 9 ∣ = 1

3 ∣ x + 5 ∣ - 2 = 0

∣ x ∣ = 925

x^{2} - x - 6 = 0

∣ 8 x - 4 ∣ = 20