What is | 7/8 x-10|<14 ?

The solution to | 7/8 x-10|<14 is -32/7 <x< 192/7

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| 7/8 x-10|<14

\frac{7}{8} x - 10 < 14

- \frac{32}{7} < x < \frac{192}{7}

Interval Notation

(- \frac{32}{7}, \frac{192}{7})

Decimal Notation

- 4.57142 \dots < x < 27.42857 \dots

Solution steps

\frac{7}{8} x - 10 < 14

Apply absolute rule: If

∣ u ∣ < a, a > 0

then

- a < u < a

- 14 < \frac{7}{8} x - 10 < 14

\frac{7}{8} x - 10 > - 14 and \frac{7}{8} x - 10 < 14

x > - \frac{32}{7} and x < \frac{192}{7}

Merge Overlapping Intervals

- \frac{32}{7} < x < \frac{192}{7}

\frac{1}{2} \cdot 3 \cdot 6

3 x + 4 = 19

- 4 x^{2} = - 36 x + 80

x^{2} + 12 x - 64 = 0

(- 125)^{\frac{1}{3}}