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

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

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

∣ x - 3 ∣ + 2 ∣ x + 1 ∣ = 4

x = - 1

Solution steps

∣ x - 3 ∣ + 2 ∣ x + 1 ∣ = 4

Find positive and negative intervals

x < - 1, - 1 \leq x < 3, x \geq 3

Solve the inequality for each interval

No Solution or x = - 1

x = - 1

2 \cdot (∣ x + 1 ∣^{2}) - ∣ x + 1 ∣ = 3

x^{2} - 4 x = 5

x^{2} + 4 x + 2 = \frac{( 5 x + 16 )}{3}

2 ∣ x + 3 ∣ = 3 ∣ x - 4 ∣

∣ 2 - x ∣ ∣ x - 7 ∣ = 36