What is | 3/4 x-1/2 |<= 1/8 ?

The solution to | 3/4 x-1/2 |<= 1/8 is 1/2 <= x<= 5/6

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| 3/4 x-1/2 |<= 1/8

\frac{3}{4} x - \frac{1}{2} \leq \frac{1}{8}

\frac{1}{2} \leq x \leq \frac{5}{6}

Solution steps

\frac{3}{4} x - \frac{1}{2} \leq \frac{1}{8}

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- \frac{1}{8} \leq \frac{3}{4} x - \frac{1}{2} \leq \frac{1}{8}

\frac{3}{4} x - \frac{1}{2} \geq - \frac{1}{8} and \frac{3}{4} x - \frac{1}{2} \leq \frac{1}{8}

x \geq \frac{1}{2} and x \leq \frac{5}{6}

Merge Overlapping Intervals

\frac{1}{2} \leq x \leq \frac{5}{6}

a^{2} + 7 ab - 18 b^{2}

(x + 4) (7 - x) (x - 5) \geq 0

n - (- 2) = - 14

64 a^{3} - 1

x^{2} - 22 x + 121 = 0

What is | 3/4 x-1/2 |<= 1/8 ?
The solution to | 3/4 x-1/2 |<= 1/8 is 1/2 <= x<= 5/6