What is the answer to |3-2x|=x+2 ?

The answer to |3-2x|=x+2 is x= 1/3 \lor x=5

Solve for x: |3-2x|=x+2

The solution is x= 1/3 \lor x=5

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∣ 3 - 2 x ∣ = x + 2

x = \frac{1}{3} or x = 5

Solution steps

∣ 3 - 2 x ∣ = x + 2

Find positive and negative intervals

x \leq \frac{3}{2}, x > \frac{3}{2}

Solve the inequality for each interval

x = \frac{1}{3} or x = 5

∣ 3 x + 2 ∣ = x + 1

∣ x - 4 ∣ + ∣ x - 8 ∣ + ∣ x - 12 ∣ = - 3

∣ x + 5 ∣ = 12

∣ 6 x - 4 ∣ (- 3) = - 9

∣ 2 x + 3 ∣ - ∣ 2 x - 5 ∣ = 6