Algebra 1 End-of-Course Review

Module Five: Inequalities

In this module, you will review how to graph inequalities on a number line and on a coordinate plane.

Inequalities

Recall that in Algebra, an inequality means the value of the variable is not equal to just one number (like in equations), but instead may be greater than or less than a number.
Inequalities have infinitely many solutions! There is no end to the numbers you can substitute into an inequality to make it true.

Solving Inequalities

Solve inequalities for the variable the same way you solve equations.

When multiplying or dividing both sides of an inequality by a negative number, you must flip the inequality symbol!

Solve and graph the following inequality examples.

Compound Inequalities

Compound inequalities are inequalities joined by the word “and” (called conjunctions) or “or” (called disjunctions).

Conjunctions (and)

Conjunctions are two inequalities connected by the word “and.”
Solutions to conjunctions have to fit the conditions of BOTH inequalities.
Conjunctions may be written separate, like “x > −3 and x < 3” or together, like “−3 < x < 3.”
If the two inequalities have no intersection in their solutions, then there are “no solutions.”

Example

Solve and graph the conjunction: –8 ≤ –2p + 4 < 10.

There are two methods that can be used to solve this inequality. Let's review each method and find the answer to this problem.

Disjunctions (or)

Disjunctions are two inequalities connected by the word “or.”
Solutions to disjunctions have to fit the conditions of EITHER of the inequalities.
Disjunctions should be written separately, like x < −3 or x > 3.
If the solutions to a disjunction cover the entire number line, the solutions are “all real numbers.”

Here are some examples of solving and graphing disjunctions as well as interpreting the graphs and writing an algebraic inequality from a given graph.

Graphing Inequalities in 2 Variables

There are three things to consider when graphing linear inequalities in two variables.