What is (|2+x|)/(|3-x|)>= 3 ?

The solution to (|2+x|)/(|3-x|)>= 3 is 7/4 <= x<3\lor 3<x<= 11/2

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(|2+x|)/(|3-x|)>= 3

\frac{∣ 2 + x ∣}{∣ 3 - x ∣} \geq 3

\frac{7}{4} \leq x < 3 or 3 < x \leq \frac{11}{2}

Solution steps

\frac{∣ 2 + x ∣}{∣ 3 - x ∣} \geq 3

Find positive and negative intervals

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

Solve the inequality for each interval

No Solution or \frac{7}{4} \leq x < 3 or 3 < x \leq \frac{11}{2}

Merge Overlapping Intervals

\frac{7}{4} \leq x < 3 or 3 < x \leq \frac{11}{2}

∣ x - 3 ∣ > - 1

∣ 6 - w ∣ < 6

∣ 3 x ∣ + 5 < 0

x^{3} - 1 > 1 - x

∣ x + 5 ∣ \geq ∣ 5 x - 7 ∣

What is (|2+x|)/(|3-x|)>= 3 ?
The solution to (|2+x|)/(|3-x|)>= 3 is 7/4 <= x<3\lor 3<x<= 11/2