Answer:
Option C. x=-3
Step-by-step explanation:
we have
[tex]-15x+60\leq 105[/tex] ----> inequality A
solve for x
subtract 60 both sides
[tex]-15x\leq 105-60[/tex]
[tex]-15x\leq 45[/tex]
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
[tex]x\geq -3[/tex]
The solution of the inequality A is the interval [-3,∞)
we have
[tex]14x+11\leq -31[/tex] ----> inequality B
Solve for x
subtract 11 both sides
[tex]14x\leq -31-11[/tex]
[tex]14x\leq -42[/tex]
Divide by 14 both sides
[tex]x\leq -3[/tex]
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
