|2x+7|<|5|

Solution

∣ 2 x + 7 ∣ < ∣ 5 ∣

- 6 < x < - 1

Interval Notation

(- 6, - 1)

Solution steps

∣ 2 x + 7 ∣ < ∣ 5 ∣

Find positive and negative intervals

x < - \frac{7}{2}, x \geq - \frac{7}{2}

Solve the inequality for each interval

- 6 < x < - \frac{7}{2} or - \frac{7}{2} \leq x < - 1

Merge Overlapping Intervals

- 6 < x < - 1

(1 + x^{2}) \geq 1 - x^{2}

∣ x + 1 ∣ + ∣ x - 4 ∣ > 7

∣ m - 1 ∣ > ∣ m + 3 ∣

\frac{1}{5 ∣ 10 x - 2 ∣} < 1

∣ 3 x - 2 ∣ > - 3