Split the compound inequality into two separate ones, then solve them individually.
{ c | 3 < c < 5 }
Practice makes perfect
We were asked to solve a compound inequality. Let's start by splitting it into separate inequalities.
Compound Inequality:& 4c-4< 8c -16 < 6c-6
First Inequality:& 4c-4 < 8c -16
Second Inequality:& 8c -16< 6c-6
Notice that compound inequalities written in this way are equivalent to compound inequalities that involve the word "and".
4c-4< 8c-16 and 8c-16< 6c-6
Let's solve the inequalities separately.
First Inequality
Inequalities can be solved in the same way as equations, by performing inverse operations on both sides until the variable is isolated. The only difference is that when you divide or multiply by a negative number, you must flip the inequality sign.
The second inequality is true for numbers less than 5. Again, we do not include 5 as the inequality sign is strict.
Compound Inequality
The solution set to the compound inequality is the intersection of the solution sets.
First Solution Set: 3 < c&
Second Solution Set: c&< 5
Intersecting Solution Set: 3 < c& < 5
