What is the answer to |3x+5|-|1+3x|=3 ?

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

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|3x+5|-|1+3x|=3

∣ 3 x + 5 ∣ - ∣ 1 + 3 x ∣ = 3

x = - \frac{1}{2}

Decimal

x = - 0.5

Solution steps

∣ 3 x + 5 ∣ - ∣ 1 + 3 x ∣ = 3

Find positive and negative intervals

x < - \frac{5}{3}, - \frac{5}{3} \leq x < - \frac{1}{3}, x \geq - \frac{1}{3}

Solve the inequality for each interval

No Solution or x = - \frac{1}{2}

x = - \frac{1}{2}

- 3 ∣ x ∣ = 12

∣ 26 - 4 x ∣ = - 2

x^{2} - 3 x - 1 = 2 + x

∣ x ∣ = 4 x + 2

∣ 45 + x ∣ = 38