What is |x+2|>|x-3|+1 ?

The solution to |x+2|>|x-3|+1 is x>1

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|x+2|>|x-3|+1

∣ x + 2 ∣ > ∣ x - 3 ∣ + 1

x > 1

Interval Notation

(1, \infty)

Solution steps

∣ x + 2 ∣ > ∣ x - 3 ∣ + 1

Find positive and negative intervals

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

Solve the inequality for each interval

No Solution or 1 < x < 3 or x \geq 3

Merge Overlapping Intervals

x > 1

4 x^{2} - 4 x = - 21

∣ 3 x - 7 ∣ \geq 8

x^{2} + 5 > 0

12 x^{2} + 5 x - 3 > 0

\frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6}