What is |x-1|+|x+1|<5 ?

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

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|x-1|+|x+1|<5

∣ x - 1 ∣ + ∣ x + 1 ∣ < 5

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

Interval Notation

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

Decimal Notation

- 2.5 < x < 2.5

Solution steps

∣ x - 1 ∣ + ∣ x + 1 ∣ < 5

Find positive and negative intervals

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

Solve the inequality for each interval

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

Merge Overlapping Intervals

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

\frac{4}{5} + \frac{3}{10}

x^{2} = 63

0 = - (x + 3)^{2} + 1

(- 4)^{- \frac{1}{2}}

3 x - 2 < 1