What is (|6-5x|)/(|x+3|)<= 1/2 ?

The solution to (|6-5x|)/(|x+3|)<= 1/2 is 9/11 <= x<= 5/3

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(|6-5x|)/(|x+3|)<= 1/2

\frac{∣ 6 - 5 x ∣}{∣ x + 3 ∣} \leq \frac{1}{2}

\frac{9}{11} \leq x \leq \frac{5}{3}

Interval Notation

[\frac{9}{11}, \frac{5}{3}]

Decimal Notation

0.81818 \dots \leq x \leq 1.66666 \dots

Solution steps

\frac{∣ 6 - 5 x ∣}{∣ x + 3 ∣} \leq \frac{1}{2}

Find positive and negative intervals

x < - 3, - 3 \leq x \leq \frac{6}{5}, x > \frac{6}{5}

Solve the inequality for each interval

No Solution or \frac{9}{11} \leq x \leq \frac{6}{5} or \frac{6}{5} < x \leq \frac{5}{3}

Merge Overlapping Intervals

\frac{9}{11} \leq x \leq \frac{5}{3}

x^{2} - 10 x - 22 = 0

\frac{2 π}{( \frac{2}{3} )}

2 x^{2} - 3 x = 2

\frac{32}{5}

\frac{147}{4} - x = 5

What is (|6-5x|)/(|x+3|)<= 1/2 ?
The solution to (|6-5x|)/(|x+3|)<= 1/2 is 9/11 <= x<= 5/3