How do you solve and write the following in interval notation: 9< -2x+3<=17?

Jul 26, 2017

Solution : $- 7 \le x < - 3$ , in interval notation: $\left[- 7 , - 3\right)$

Explanation:

$9 < - 2 x + 3 \le 17 \mathmr{and} 9 - 3 < - 2 x + 3 - 3 \le 17 - 3$ or

$6 < - 2 x \le 14 \mathmr{and} 3 < - x \le 7 \mathmr{and} - 3 > x \ge - 7$ or

$- 7 \le x < - 3$ , x lies between $\left[- 7 \mathmr{and} - 3\right)$.

Note: When mutiplied or divided by negative quantity the inequality

sign reverses.

Solution : $- 7 \le x < - 3$ , in interval notation $\left[- 7 , - 3\right)$ [Ans]