1. Two inequalities that are joined by the word “and” or the word “or”
Solving Compound Inequalities Containing “AND”
Compound Inequality:
Solutions of Compound Inequalities joined by “AND”:
It is read:
The graph shows that the OVERLAP of the solutions is the
solution to the compound inequality!
Write the compound inequality that represents each situation. Then graph it to show the solutions.
1. Today’s temperature will be above 32°F, but not as high as 40°F.
2. The books were priced between $3.50 and $6.00, inclusive.
Two inequalities that are joined by the word “and” or the word “or”
Any number that makes
BOTH inequalities true
“x is greater than or equal to -5 and less than or equal to 7”
OR “x is between -5 and 7, inclusive”

2. You can solve compound inequalities involving “AND” two different ways:
Solve each inequality and graph your solutions.
You can separate the inequality into two pieces.
(HINT: the middle expression is found in both pieces)
Solve each separately.
Draw graphs of each. The solution is the overlap!
Isolate the variable between the two inequality signs.
*Instead of just doing the “same thing to both sides,” you must do the same thing to ALL THREE “SIDES”
Separate into two inequalities.
Draw graphs of each. The solution is the overlap!