What is -9|-7v+3|>-27 ?

The solution to -9|-7v+3|>-27 is 0<v< 6/7

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-9|-7v+3|>-27

- 9 ∣ - 7 v + 3 ∣ > - 27

0 < v < \frac{6}{7}

Interval Notation

(0, \frac{6}{7})

Decimal Notation

0 < v < 0.85714 \dots

Solution steps

- 9 ∣ - 7 v + 3 ∣ > - 27

Multiply both sides by

- 1

9 ∣ - 7 v + 3 ∣ < 27

Divide both sides by

9

∣ - 7 v + 3 ∣ < 3

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- 3 < - 7 v + 3 < 3

- 7 v + 3 > - 3 and - 7 v + 3 < 3

v < \frac{6}{7} and v > 0

Merge Overlapping Intervals

0 < v < \frac{6}{7}

\frac{1}{2} x + \frac{3}{2} x + 6 x - 3 x

∣ 3 + 2 ∣ \leq 7

\frac{1}{12} - \frac{7}{15}

2 y + 4 = 0

\frac{3 x + 1}{x - 7} \leq 0