Answer:
The solution is [tex]x>\frac{4}{3}[/tex]
Step-by-step explanation:
A compound inequality is an inequality that combines two simple inequalities.
We want to solve for x the following compound inequality
[tex]3x-91>-87 \:{OR} \:{21x-17>25}[/tex]
Solving the first inequality for x, we get:
[tex]3x-91+91>-87+91\\\\3x>4\\\\x>\frac{4}{3}[/tex]
Solving the second inequality for x, we get:
[tex]21x-17+17>25+17\\\\21x>42\\\\x>2[/tex]
So our compound inequality can be expressed as the simple inequality:
[tex]x>\frac{4}{3}[/tex]
The graph of a compound inequality with an "or" represents the union of the graphs of the inequalities. A number is a solution to the compound inequality if the number is a solution to at least one of the inequalities.
Graphically, we get
