What is |x-2|+|x-3|<6 ?

The solution to |x-2|+|x-3|<6 is -1/2 <x< 11/2

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|x-2|+|x-3|<6

∣ x - 2 ∣ + ∣ x - 3 ∣ < 6

- \frac{1}{2} < x < \frac{11}{2}

Interval Notation

(- \frac{1}{2}, \frac{11}{2})

Decimal Notation

- 0.5 < x < 5.5

Solution steps

∣ x - 2 ∣ + ∣ x - 3 ∣ < 6

Find positive and negative intervals

x < 2, 2 \leq x < 3, x \geq 3

Solve the inequality for each interval

- \frac{1}{2} < x < 2 or 2 \leq x < 3 or 3 \leq x < \frac{11}{2}

Merge Overlapping Intervals

- \frac{1}{2} < x < \frac{11}{2}

x^{2} - 1 \leq ∣ 2 x - 1 ∣

\frac{x}{( x ^{2} - x - 1 )} < 2

∣ 4 x - 3 ∣ + 2 < 10

\frac{2}{∣ x - 4 ∣} > 1

lo g_{2} (∣ x - 2 ∣) > lo g_{2} (∣ x + 4 ∣)