Solve the compound inequality
5x + 11 > -9 and 10x - 3 < 27
To solve compound inequalities, we will solve each inequality separately and then find the intersection of the solution sets.
Starting with the first inequality:
5x + 11 > -9
Subtract 11 from both sides:
5x > -20
To isolate x, divide both sides by 5:
x > -4
Now, let's solve the second inequality:
10x - 3 < 27
Add 3 to both sides:
10x < 30
Divide both sides by 10 to isolate x:
x < 3
Now, we need to find the intersection of the solution sets. Since x can be greater than -4 and less than 3, the solution set is:
-4 < x < 3