What is |x-2|>2+x-|3-x| ?

The solution to |x-2|>2+x-|3-x| is x 7

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|x-2|>2+x-|3-x|

∣ x - 2 ∣ > 2 + x - ∣ 3 - x ∣

x < 1 or x > 7

Interval Notation

(- \infty, 1) \cup (7, \infty)

Solution steps

∣ x - 2 ∣ > 2 + x - ∣ 3 - x ∣

Find positive and negative intervals

x < 2, 2 \leq x \leq 3, x > 3

Solve the inequality for each interval

x < 1 or No Solution or x > 7

Merge Overlapping Intervals

x < 1 or x > 7

∣ x - 1 ∣ + ∣ x - 2 ∣ + ∣ x - 3 ∣ \leq 6

\frac{1}{∣ x - 2 ∣} \geq \frac{1}{4}

\frac{5}{( 3 - x )} > 1

4 ∣ x - 2 ∣ - 2 - x < 4 x + 1

∣ x - 6 ∣ \geq 4