What is (|x-3|)/(|x+1|)<= 1 ?

The solution to (|x-3|)/(|x+1|) = 1

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(|x-3|)/(|x+1|)<= 1

\frac{∣ x - 3 ∣}{∣ x + 1 ∣} \leq 1

x \geq 1

Interval Notation

[1, \infty)

Solution steps

\frac{∣ x - 3 ∣}{∣ x + 1 ∣} \leq 1

Find positive and negative intervals

x < - 1, - 1 \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

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

∣ x ∣ < 2

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

\frac{1}{x - 2} < 4

∣ x - 5 ∣ + ∣ x + 4 ∣ \leq 7