What is |x-1|+|x-2|<7 ?

The solution to |x-1|+|x-2|<7 is -2<x<5

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|x-1|+|x-2|<7

∣ x - 1 ∣ + ∣ x - 2 ∣ < 7

- 2 < x < 5

Interval Notation

(- 2, 5)

Solution steps

∣ x - 1 ∣ + ∣ x - 2 ∣ < 7

Find positive and negative intervals

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

Solve the inequality for each interval

- 2 < x < 1 or 1 \leq x < 2 or 2 \leq x < 5

Merge Overlapping Intervals

- 2 < x < 5

\frac{( x - 2 )}{( 3 )} < 2

x^{2} + 4 x + 3 > x + 3

∣ x ∣ + x^{2} > 0

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

∣ 3 x + 5 ∣ \leq \frac{7}{2}