Final answer:
To solve the given system of inequalities, solve each inequality separately. The solution to the system is x < -16/9 and x ≤ -19/13.
Step-by-step explanation:
To solve the given system of inequalities, we need to solve each inequality separately:
-9x + 2 > 18
Add 9x to both sides to isolate the variable:
2 > 18 + 9x
Subtract 18 from both sides:
-16 > 9x
Divide both sides by 9 (remember to change the direction of the inequality when dividing by a negative number):
x < -16/9
13x + 15 ≤ -4
Subtract 15 from both sides to isolate the variable:
13x ≤ -4 - 15
Simplify:
13x ≤ -19
Divide both sides by 13:
x ≤ -19/13
Therefore, the solution to the system of inequalities is:
x < -16/9 and x ≤ -19/13