What is |x+1|+|x+2|<= 10 ?

The solution to |x+1|+|x+2|<= 10 is -13/2 <= x<= 7/2

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|x+1|+|x+2|<= 10

∣ x + 1 ∣ + ∣ x + 2 ∣ \leq 10

- \frac{13}{2} \leq x \leq \frac{7}{2}

Solution steps

∣ x + 1 ∣ + ∣ x + 2 ∣ \leq 10

Find positive and negative intervals

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

Solve the inequality for each interval

- \frac{13}{2} \leq x < - 2 or - 2 \leq x < - 1 or - 1 \leq x \leq \frac{7}{2}

Merge Overlapping Intervals

- \frac{13}{2} \leq x \leq \frac{7}{2}

\frac{3 ∣ x ∣ - 2}{∣ x ∣ - 1} \geq 2

x ∣ x + 1 ∣ + ∣ x ∣ > 3

∣ 3 - 5 x ∣ \leq 10

\frac{( 2 - ∣ x ∣ )}{∣ 2 + x ∣} \leq \frac{3}{( ∣ x ∣ - 1 )}

x^{2} - 3 x + 2 + 2 x - 1 < 0