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

The solution to |x-3|-|x+2| =-1

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|x-3|-|x+2|<= 3

∣ x - 3 ∣ - ∣ x + 2 ∣ \leq 3

x \geq - 1

Interval Notation

[- 1, \infty)

Solution steps

∣ x - 3 ∣ - ∣ x + 2 ∣ \leq 3

Find positive and negative intervals

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

Solve the inequality for each interval

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

Merge Overlapping Intervals

x \geq - 1

\frac{3 - ( 5 x - 2 )}{4} \leq 8

\frac{∣ x - 3 ∣}{∣ x + 1 ∣} \leq 1

x^{3} - 1 \geq 1 - x

∣ x ∣ < 2

x^{2} - 2 x + 3 < - 3