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

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

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|u+2|+|u-3|=5

∣ u + 2 ∣ + ∣ u - 3 ∣ = 5

- 2 \leq u \leq 3

Solution steps

∣ u + 2 ∣ + ∣ u - 3 ∣ = 5

Find positive and negative intervals

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

Solve the inequality for each interval

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

Merge Overlapping Intervals

- 2 \leq u \leq 3

x^{2} + 4 x + 3 = x + 1

∣ x - 3 ∣ + x = 7

∣ x - 4 ∣ + ∣ 2 x + 1 ∣ - ∣ 3 x ∣ = 3

x^{2} - x - 12 = x + 12 - x^{2}

∣ 6 x + 9 ∣ = ∣ 3 x - 7 ∣