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

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

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

∣ x - 3 ∣ - ∣ x + 2 ∣ \geq 2

x \leq - \frac{1}{2}

Interval Notation

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

Decimal Notation

x \leq - 0.5

Solution steps

∣ x - 3 ∣ - ∣ x + 2 ∣ \geq 2

Find positive and negative intervals

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

Solve the inequality for each interval

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

Merge Overlapping Intervals

x \leq - \frac{1}{2}

- 1 - 4

x^{2} - 121 = 0

12 5^{\frac{3}{4}} \cdot 5^{\frac{3}{4}}

∣ 10 - 4 x ∣ \geq 12

x^{2} - 9 x - 15 = - 5