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

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

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

\frac{∣ 3 x + 1 ∣}{∣ x ∣} \leq 3

x \leq - \frac{1}{6}

Solution steps

\frac{∣ 3 x + 1 ∣}{∣ x ∣} \leq 3

Find positive and negative intervals

x < - \frac{1}{3}, - \frac{1}{3} \leq x < 0, x \geq 0

Solve the inequality for each interval

x < - \frac{1}{3} or - \frac{1}{3} \leq x \leq - \frac{1}{6} or No Solution

Merge Overlapping Intervals

x \leq - \frac{1}{6}

3 x + 6 \geq 12

∣ 3 t + 4 ∣ + 3 = 8

\frac{v}{11.6} = - 11.2

\frac{7 x + 8}{2} = 9 x + 1

4 x - 5 = 27