Question

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

Answer 1

Solution : `-7 <= x < -3` , in interval notation: `[-7,-3)`

Explanation:

`9 < -2x +3 <= 17 or 9-3 < -2x +3-3 <= 17 -3` or

`6 < -2x <= 14 or 3 < -x <= 7 or -3 > x >= -7` or

`-7 <= x < -3` , x lies between `[-7 and -3)`.

Note: When mutiplied or divided by negative quantity the inequality

sign reverses.

Solution : `-7 <= x < -3` , in interval notation `[-7,-3)` [Ans]