We were asked to solve a compound inequality. Let's start by splitting it into separate inequalities.
Compound Inequality:& 22< -3c+ 4 < 14
First Inequality:& 22< -3c+ 4
Second Inequality:& -3c+ 4 < 14
Notice that compound inequalities written in this way are equivalent to compound inequalities that involve the word and.
22< -3c+ 4 and -3c+ 4 < 14
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.
This inequality tells us that all values greater than - 103 will satisfy the inequality.
Note that the point on - 103 is open because it is not included in the solution set.
Compound Inequality
The solution set to the compound inequality is the intersection of the solution sets. To help visualize the algebraic expression, we will write c>- 103 as - 103cannot be greater than - 103 and less than -6 simultaneously, the compound inequality does not have a solution.
