What is the answer to |x+1|+|x-2|+|x-5|=x+4 ?

The answer to |x+1|+|x-2|+|x-5|=x+4 is 2<= x<= 5

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|x+1|+|x-2|+|x-5|=x+4

∣ x + 1 ∣ + ∣ x - 2 ∣ + ∣ x - 5 ∣ = x + 4

2 \leq x \leq 5

Solution steps

∣ x + 1 ∣ + ∣ x - 2 ∣ + ∣ x - 5 ∣ = x + 4

Find positive and negative intervals

x < - 1, - 1 \leq x < 2, 2 \leq x < 5, x \geq 5

Solve the inequality for each interval

No Solution or 2 \leq x < 5 or x = 5

Merge Overlapping Intervals

2 \leq x \leq 5

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

12 + 3 ∣ x + 3 ∣ = 9 x - 9

∣ 1 - 2 x ∣ = - 2 x

- 14 ∣ 3 x + 6 ∣ = - 28

x^{2} + 1 - x^{2} - 1 = 0

What is the answer to |x+1|+|x-2|+|x-5|=x+4 ?
The answer to |x+1|+|x-2|+|x-5|=x+4 is 2<= x<= 5
Solve for x: |x+1|+|x-2|+|x-5|=x+4
The solution is 2<= x<= 5