What is the answer to |2x+3|-|2x-5|=6 ?

The answer to |2x+3|-|2x-5|=6 is x=2

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|2x+3|-|2x-5|=6

∣ 2 x + 3 ∣ - ∣ 2 x - 5 ∣ = 6

x = 2

Solution steps

∣ 2 x + 3 ∣ - ∣ 2 x - 5 ∣ = 6

Find positive and negative intervals

x < - \frac{3}{2}, - \frac{3}{2} \leq x < \frac{5}{2}, x \geq \frac{5}{2}

Solve the inequality for each interval

No Solution or x = 2

x = 2

x^{2} + x - 5 = ∣ 4 x - 1 ∣

∣ x - 2 ∣ = x^{2}

(x^{2} + x + 2) + ∣ x + 1 ∣ = 5

∣ x - 1 ∣ - ∣ x - 2 ∣ + ∣ x - 3 ∣ = 5 x - 1

\frac{( 3 x + 4 )}{3} = 7