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

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

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

∣ x + 2 ∣ + ∣ x - 3 ∣ = 5

- 2 \leq x \leq 3

Solution steps

∣ x + 2 ∣ + ∣ x - 3 ∣ = 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

2 x^{2} + 4 x = 96

x - x^{2} = 6

\frac{4}{\frac{1}{2}}

\frac{4}{5} (10 u + 65) \geq \frac{6}{5} (5 u - 10) + 4 u

(- x)^{2}