# How do you solve and write the following in interval notation: − 1/2 ≤ (4 − 3x) / 5 ≤ 1/4?

Jul 21, 2017

Solution: $\frac{11}{12} \le x \le \frac{26}{12}$ , in interval notation: $\left[\frac{11}{12} , \frac{26}{12}\right]$

#### Explanation:

$- \frac{1}{2} \le \frac{4 - 3 x}{5} \le \frac{1}{4}$ (multiplying by $20$)

$- 10 \le 4 \left(4 - 3 x\right) \le 5$ or

-10 <= 16-12x) <= 5  (adding $- 16$)

$- 26 \le - 12 x \le - 11$ (dividing by $12$)

$- \frac{26}{12} \le - x \le - \frac{11}{12}$ (multiplying by $- 1$)

$\frac{26}{12} \ge x \ge \frac{11}{12} \mathmr{and} \frac{11}{12} \le x \le \frac{26}{12}$

Solution: $\frac{11}{12} \le x \le \frac{26}{12}$ , in interval notation $\left[\frac{11}{12} , \frac{26}{12}\right]$ [Ans]