What is |x+1|+|x-2|<= 4 ?

The solution to |x+1|+|x-2|<= 4 is -3/2 <= x<= 5/2

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|x+1|+|x-2|<= 4

∣ x + 1 ∣ + ∣ x - 2 ∣ \leq 4

- \frac{3}{2} \leq x \leq \frac{5}{2}

Solution steps

∣ x + 1 ∣ + ∣ x - 2 ∣ \leq 4

Find positive and negative intervals

x < - 1, - 1 \leq x < 2, x \geq 2

Solve the inequality for each interval

- \frac{3}{2} \leq x < - 1 or - 1 \leq x < 2 or 2 \leq x \leq \frac{5}{2}

Merge Overlapping Intervals

- \frac{3}{2} \leq x \leq \frac{5}{2}

\frac{201 8 ^{2018}}{20}

- 7 - 9 ∣ 2 x + 8 ∣ < - 16

9 y - 40 > - 4 (3 - 4 y)

\frac{11}{12} - \frac{2}{3}

5 w^{2} - 8 = - 53