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

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

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

\frac{∣ 3 x + 1 ∣}{∣ x + 3 ∣} < 1

- 1 < x < 1

Solution steps

\frac{∣ 3 x + 1 ∣}{∣ x + 3 ∣} < 1

Find positive and negative intervals

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

Solve the inequality for each interval

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

Merge Overlapping Intervals

- 1 < x < 1

- 1 y = - 69

4. 3^{2}

405 \cdot \frac{π}{180}

6 \cdot (- \frac{5}{2})

x^{2} + 3 x + 7 > 0