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

Answer:

Option D.

$x\geq -2$  or  $x\leq -6$

Step-by-step 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  $x\leq -6$