What is the answer to |x-3|+|x+2|=5 ?

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

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|x-3|+|x+2|=5

∣ x - 3 ∣ + ∣ x + 2 ∣ = 5

- 2 \leq x \leq 3

Solution steps

∣ x - 3 ∣ + ∣ x + 2 ∣ = 5

Find positive and negative intervals

x < - 2, - 2 \leq x < 3, x \geq 3

Solve the inequality for each interval

No Solution or - 2 \leq x < 3 or x = 3

Merge Overlapping Intervals

- 2 \leq x \leq 3

3 ∣ 2 x + 9 ∣ + 12 = 10

∣ 5 x + 1 ∣ = 2

- 13 + 11 ∣ - 10 x + 13 ∣ = 16

∣ y ∣ = 1 - ∣ x ∣

∣ x ∣ + 5 = 11