8>|6x-1|>7

Solution

8 > ∣ 6 x - 1 ∣ > 7

- \frac{7}{6} < x < - 1 or \frac{4}{3} < x < \frac{3}{2}

Interval Notation

(- \frac{7}{6}, - 1) \cup (\frac{4}{3}, \frac{3}{2})

Decimal Notation

- 1.16666 \dots < x < - 1 or 1.33333 \dots < x < 1.5

Solution steps

8 > ∣ 6 x - 1 ∣ > 7

a > u > b

then

a > u and u > b

8 > ∣ 6 x - 1 ∣ and ∣ 6 x - 1 ∣ > 7

8 > ∣ 6 x - 1 ∣ : - \frac{7}{6} < x < \frac{3}{2}

∣ 6 x - 1 ∣ > 7 : x < - 1 or x > \frac{4}{3}

Combine the intervals

- \frac{7}{6} < x < \frac{3}{2} and (x < - 1 or x > \frac{4}{3})

Merge Overlapping Intervals

- \frac{7}{6} < x < - 1 or \frac{4}{3} < x < \frac{3}{2}

(\frac{x ^{- 11} y ^{- 2}}{z ^{8}})^{- 4}

\frac{5}{6} + \frac{7}{8}

- 16 t^{2} + 50 t - 36

\frac{1}{x} - \frac{1}{x - 1} > 0

∣ x - 3 ∣ \leq 7