What is |x-3|+|x+2|<11 ?

The solution to |x-3|+|x+2|<11 is -5<x<6

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|x-3|+|x+2|<11

∣ x - 3 ∣ + ∣ x + 2 ∣ < 11

- 5 < x < 6

Interval Notation

(- 5, 6)

Solution steps

∣ x - 3 ∣ + ∣ x + 2 ∣ < 11

Find positive and negative intervals

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

Solve the inequality for each interval

- 5 < x < - 2 or - 2 \leq x < 3 or 3 \leq x < 6

Merge Overlapping Intervals

- 5 < x < 6

\frac{4 π}{2 π}

x^{4} + a^{2} x^{2} + b^{2} x^{2} + a^{2} b^{2}

12 x^{3} - 36 x^{2} + 27 x - 75 x y^{2}

(x^{\frac{1}{2}})^{\frac{2}{3}}

25 m^{2} + 10 m + 1