What is | 3/4 x+1/3 |<= 1/12 ?

The solution to | 3/4 x+1/3 |<= 1/12 is -5/9 <= x<=-1/3

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| 3/4 x+1/3 |<= 1/12

\frac{3}{4} x + \frac{1}{3} \leq \frac{1}{12}

- \frac{5}{9} \leq x \leq - \frac{1}{3}

Solution steps

\frac{3}{4} x + \frac{1}{3} \leq \frac{1}{12}

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

- \frac{1}{12} \leq \frac{3}{4} x + \frac{1}{3} \leq \frac{1}{12}

\frac{3}{4} x + \frac{1}{3} \geq - \frac{1}{12} and \frac{3}{4} x + \frac{1}{3} \leq \frac{1}{12}

x \geq - \frac{5}{9} and x \leq - \frac{1}{3}

Merge Overlapping Intervals

- \frac{5}{9} \leq x \leq - \frac{1}{3}

- 4 < 8

x^{4} + 12 x^{3} + 31 x^{2} - 12 x - 32

3 x^{2} + 6 x + 2 = 0

(3 - 2)^{2}

t^{2} - 2 t - 2 = 0

What is | 3/4 x+1/3 |<= 1/12 ?
The solution to | 3/4 x+1/3 |<= 1/12 is -5/9 <= x<=-1/3