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

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

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

∣ x + 3 ∣ + ∣ x - 2 ∣ = 5

- 3 \leq x \leq 2

Solution steps

∣ x + 3 ∣ + ∣ x - 2 ∣ = 5

Find positive and negative intervals

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

Solve the inequality for each interval

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

Merge Overlapping Intervals

- 3 \leq x \leq 2

x^{2} + x + 1 + ∣ 2 x - 3 ∣ = 4 x

∣ - 13 ∣ + \frac{3 x + 6}{7} + ∣ 4 ∣ = 25

∣ x + 3 ∣ - ∣ 4 - x ∣ = ∣ 8 + x ∣

∣ x - 3 ∣ + ∣ x + 5 ∣ = 8

x^{2} = ∣ x ∣