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

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

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|x-2|=2x+3

∣ x - 2 ∣ = 2 x + 3

x = - \frac{1}{3}

Decimal

x = - 0.33333 \dots

Solution steps

∣ x - 2 ∣ = 2 x + 3

Find positive and negative intervals

x < 2, x \geq 2

Solve the inequality for each interval

x = - \frac{1}{3} or No Solution

x = - \frac{1}{3}

∣ x - 3 ∣ = 4 x - 7

∣ x - 3 ∣ + ∣ x - 1 ∣ = 5

∣ x - 3 ∣ + ∣ x - 1 ∣ = 2

∣ 2 x + 3 ∣ - ∣ x + 4 ∣ = 6

y, ∣ x ∣ - y = 4