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

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

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|x+1|+|x+2|<2

∣ x + 1 ∣ + ∣ x + 2 ∣ < 2

- \frac{5}{2} < x < - \frac{1}{2}

Interval Notation

(- \frac{5}{2}, - \frac{1}{2})

Decimal Notation

- 2.5 < x < - 0.5

Solution steps

∣ x + 1 ∣ + ∣ x + 2 ∣ < 2

Find positive and negative intervals

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

Solve the inequality for each interval

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

Merge Overlapping Intervals

- \frac{5}{2} < x < - \frac{1}{2}

y - 12 \geq - (2 y - 3)

4 x^{2} - 2 x = 1

4 x^{2} + 16 x + 16

\frac{3}{4} \cdot \frac{3}{4}

\frac{1}{4} t = 3