What is the answer to 1/4 |x-2|=2x+3 ?

The answer to 1/4 |x-2|=2x+3 is x=-10/9

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1/4 |x-2|=2x+3

\frac{1}{4} ∣ x - 2 ∣ = 2 x + 3

x = - \frac{10}{9}

Decimal

x = - 1.11111 \dots

Solution steps

\frac{1}{4} ∣ x - 2 ∣ = 2 x + 3

Find positive and negative intervals

x < 2, x \geq 2

Solve the inequality for each interval

x = - \frac{10}{9} or No Solution

x = - \frac{10}{9}

∣ 5 x - 2 ∣ = 6

x^{2} - 4 x - 8 = 4

∣ 3 x + 12 ∣ = 9 x

x^{2} + x - 4 = 2

∣ x + 1 ∣ + 2 = 7