What is |x+2|+|x-3|<7 ?

The solution to |x+2|+|x-3|<7 is -3<x<4

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|x+2|+|x-3|<7

∣ x + 2 ∣ + ∣ x - 3 ∣ < 7

- 3 < x < 4

Interval Notation

(- 3, 4)

Solution steps

∣ x + 2 ∣ + ∣ x - 3 ∣ < 7

Find positive and negative intervals

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

Solve the inequality for each interval

- 3 < x < - 2 or - 2 \leq x < 3 or 3 \leq x < 4

Merge Overlapping Intervals

- 3 < x < 4

\frac{x}{3} + 3 = 7

\frac{3 ( 2 x + 7 )}{- 3} > x + 1

x^{2} - 2 x + 16 = 0

- 7 + x = 13

x - 2 = 15 x + 8 - 9 x