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

The answer to |2x-3|+|x+1|=|x+4| is x=0\lor x=3

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

∣ 2 x - 3 ∣ + ∣ x + 1 ∣ = ∣ x + 4 ∣

x = 0 or x = 3

Solution steps

∣ 2 x - 3 ∣ + ∣ x + 1 ∣ = ∣ x + 4 ∣

Find positive and negative intervals

x < - 4, - 4 \leq x < - 1, - 1 \leq x < \frac{3}{2}, x \geq \frac{3}{2}

Solve the inequality for each interval

No Solution or x = 0 or x = 3

x = 0 or x = 3

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

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

∣ 2 + x ∣ = ∣ x - 8 ∣

∣ 3 x + 1 ∣ = x - 2

\frac{( x - 3 )}{4}^{2} = \frac{9}{4}

What is the answer to |2x-3|+|x+1|=|x+4| ?
The answer to |2x-3|+|x+1|=|x+4| is x=0\lor x=3
Solve for x: |2x-3|+|x+1|=|x+4|
The solution is x=0\lor x=3