What is the answer to |2x+1|=|x+5| ?

The answer to |2x+1|=|x+5| is x=-2\lor x=4

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|2x+1|=|x+5|

∣ 2 x + 1 ∣ = ∣ x + 5 ∣

x = - 2 or x = 4

Solution steps

∣ 2 x + 1 ∣ = ∣ x + 5 ∣

Find positive and negative intervals

x < - 5, - 5 \leq x < - \frac{1}{2}, x \geq - \frac{1}{2}

Solve the inequality for each interval

No Solution or x = - 2 or x = 4

x = - 2 or x = 4

∣ x - 2 ∣ = ∣ x + 3 ∣

∣ - 2 x ∣ - ∣ - 8 ∣ = 0

∣ x + 4 ∣ - 6 = 2

5 = ∣ b + 5 ∣

∣ - x ∣ = ∣ 1 ∣