Question

Solve for x

-15x+60 <_105 AND 14x+11<_-31

A. x<_-3
B. x>_-3
C. x=-3
D. There are no solutions
E. All values of x are solutions

Answer 1

Option C. x=-3

Explanation:

we have

`-15x+60\leq 105` ----> inequality A

solve for x

subtract 60 both sides

`-15x\leq 105-60`

`-15x\leq 45`

Divide by -15 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\geq -3`

The solution of the inequality A is the interval [-3,∞)

we have

`14x+11\leq -31` ----> inequality B

Solve for x

subtract 11 both sides

`14x\leq -31-11`

`14x\leq -42`

Divide by 14 both sides

`x\leq -3`

The solution of the inequality B is the interval (-∞,-3]

The solution of the system is

(-∞,-3] ∩ [-3,∞) =-3

therefore

The solution is x=-3