What is the answer to |x+2|+|x+5|-|x-7|=15 ?

The answer to |x+2|+|x+5|-|x-7|=15 is x=-29\lor x=5

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|x+2|+|x+5|-|x-7|=15

∣ x + 2 ∣ + ∣ x + 5 ∣ - ∣ x - 7 ∣ = 15

x = - 29 or x = 5

Solution steps

∣ x + 2 ∣ + ∣ x + 5 ∣ - ∣ x - 7 ∣ = 15

Find positive and negative intervals

x < - 5, - 5 \leq x < - 2, - 2 \leq x < 7, x \geq 7

Solve the inequality for each interval

x = - 29 or No Solution or x = 5

x = - 29 or x = 5

x^{2} - x + 3 = x^{2} - 4 x + 7

∣ x + 3 ∣ - 5 = 4

∣ x - 1 ∣ + ∣ x - 3 ∣ = \frac{3}{2}

∣ x + 3 ∣ + 3 = 3

4 x^{2} - 1 = 4 x^{2} - 1

What is the answer to |x+2|+|x+5|-|x-7|=15 ?
The answer to |x+2|+|x+5|-|x-7|=15 is x=-29\lor x=5
Solve for x: |x+2|+|x+5|-|x-7|=15
The solution is x=-29\lor x=5