What is | 2/3 x+1/2 |<= 1/6 ?

The solution to | 2/3 x+1/2 |<= 1/6 is -1<= x<=-1/2

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| 2/3 x+1/2 |<= 1/6

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

- 1 \leq x \leq - \frac{1}{2}

Solution steps

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

Apply absolute rule: If

∣ u ∣ \leq a, a > 0

then

- a \leq u \leq a

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

\frac{2}{3} x + \frac{1}{2} \geq - \frac{1}{6} and \frac{2}{3} x + \frac{1}{2} \leq \frac{1}{6}

x \geq - 1 and x \leq - \frac{1}{2}

Merge Overlapping Intervals

- 1 \leq x \leq - \frac{1}{2}

81 x^{2} + 90 x + 25 = 0

18 x^{2} + 12 x + 2

x + 1 x - 1 \leq 0

x^{2} - \frac{2}{5} x + \frac{1}{25}

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

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