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

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

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|x+3|>|x-2|

∣ x + 3 ∣ > ∣ x - 2 ∣

x > - \frac{1}{2}

Interval Notation

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

Decimal Notation

x > - 0.5

Solution steps

∣ x + 3 ∣ > ∣ x - 2 ∣

Find positive and negative intervals

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

Solve the inequality for each interval

No Solution or - \frac{1}{2} < x < 2 or x \geq 2

Merge Overlapping Intervals

x > - \frac{1}{2}

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

x^{2} - 49 = 48 x

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

3 (4 + 12 x) - 6 (2 x + 3) = 36 + 2 (3 x + 2)

x^{2} - 100 \geq 0