Question

Solve -(2)/(3)x > 8 or -(2)/(3)x < 4

Ax
Bx
Cx

Answer 1

Option B. x < -12 or x > -6

Explanation:

we have

`-(2)/(3)x>8` ---> inequality A

Solve for x

Multiply by -3/2 both sides

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

so

`x < (-(3)/(2))8`

`x < -12`

The solution of the inequality A is the interval (-∞,-12)

`-(2)/(3)x<4` ----> inequality B

Solve for x

Multiply by -3/2 both sides

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

so

`x > (-(3)/(2))4`

`x >-6`

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

therefore

The solution of the system

`-(2)/(3)x>8` or
`-(2)/(3)x<4` is equal to

(-∞,-12) ∪ (-6,∞)

x