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Popular >

|x-3|<|x-2|

Solution

∣ x - 3 ∣ < ∣ x - 2 ∣

Solution

x > \frac{5}{2}

+2

Interval Notation

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

Decimal Notation

x > 2.5

Solution steps

∣ x - 3 ∣ < ∣ x - 2 ∣

Find positive and negative intervals

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

Solve the inequality for each interval

No Solution or \frac{5}{2} < x < 3 or x \geq 3

Merge Overlapping Intervals

x > \frac{5}{2}

Popular Examples

∣ 2 x - 3 ∣ < ∣ x - 5 ∣

((3-|x|))/((|x|-5))>0

\frac{( 3 - ∣ x ∣ )}{( ∣ x ∣ - 5 )} > 0

- 5 ∣ x - 3 ∣ - 5 < 15

∣ 4 x - 3 ∣ \leq 4 - 3 x

∣ x - 28 ∣ \leq 2

Frequently Asked Questions (FAQ)

What is |x-3|<|x-2| ?
The solution to |x-3|<|x-2| is x> 5/2