Solving Inequalities
Solving MultiStep Inequalities
Inequalities involving more than one operation can be solved
by undoing theoperations in reverse order in the same way you
would solve an equation withmore than one operation. The
important exception is that multiplying ordividing an inequality
by a negative number reverses the sign of the inequality.
Example
Solve 3 f  7  f + 9.
Solution
3 f  7  f + 9 

3 f  7 + f  f + 9 + f 
Add f to each side. 
2f  7 9 
Combine like terms. 
2f  7 + 7 9 + 7 
Add 7 to each side. 
2f 16 
Combine like terms. 

Divide each side by 2 and change to . 
f 8 

The solution set is {f  f 8} 

Solving Compound Inequalities
Two inequalities considered together form a compound
inequality.
AND Compound
Inequalities

Compound inequalities that contain
theword and are true only if both
inequalities are true. The graph of a compound inequality
containing and is the intersection of the graphs of the
two inequalities that makeup the compound inequality. To
find the intersection, determine where the two graphs
overlap. 
OR Compound
Inequalities

Compound inequalities that contain the
word or are true if one or more of the
inequalities is true. The graph is the union of the
graphs of the two inequalities that make up the compound
inequality. 
