Question

Which of the following is the solution to the compound inequality below?

3x+5 -1 or -2x-7 5

x left-2 or x right-6

Answer 1

Option D.

`x\geq -2` or
`x\leq -6`

Explanation:

The correct question in the attached figure

we have

`3x+5\geq -1` ----> inequality A

subtract 5 both sides

`3x\geq -1-5`

`3x\geq -6`

divide by 3 both sides

`x\geq -2`

The solution of the inequality A is the interval [-2,∞)

`-2x-7\geq 5` ----> inequality B

adds 7 both sides

`-2x\geq 5+7`

`-2x\geq 12`

divide by -2 both sides

Remember that when you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality symbol

`x\leq -6`

The solution of the inequality B is the interval (-∞,-6]

therefore

The solution of the system is

`x\geq -2` or
`x\leq -6`