Solve\:the\:compound\:inequality\:5x\:+\:11\:\ge \:-9\:and\:\:10x\:-\:3\:\le \:27
To solve the compound inequality 5x + 11 ≥ -9 and 10x - 3 ≤ 27, we will first solve each inequality separately and then find the intersection of their solution sets.
Solving the first inequality:
5x + 11 ≥ -9
Subtract 11 from both sides of the inequality:
5x ≥ -9 - 11
5x ≥ -20
Divide both sides by 5 (remember to reverse the inequality sign when dividing by a negative number):
x ≥ -4
Solving the second inequality:
10x - 3 ≤ 27
Add 3 to both sides of the inequality:
10x ≤ 27 + 3
10x ≤ 30
Divide both sides by 10:
x ≤ 3
The intersection of the solution sets of the two inequalities is the solution to the compound inequality.
Therefore, x ≥ -4 and x ≤ 3.
Or, combining the two inequalities:
-4 ≤ x ≤ 3