Solving and Graphing Inequalities Joined by And or Or

Examples, videos, and solutions to help Algebra I students learn how to solve inequalities joined by “and” or “or”.

New York State Common Core Math Algebra I, Module 1, Lesson 16

Worksheets for Algebra 1

Printable “Linear Inequality” worksheets:
Solve 1-step inequalities (addition & subtraction)
Solve 1-step inequalities (multiplication & division)
Solve 1-step inequalities (all operations)
Solve linear inequalities (include number lines)
Graph compound inequalities on the number line
Solve & graph compound inequalities

Lesson 16 Student Outcomes

• Students solve two inequalities joined by “and” or “or,” then graph the solution set on the number line.
• “And” and “Or” Statements

Recall that for a statement separated by “and” to be true BOTH statements must be true.
If it is separated by “or,” at least one statement must be true.

Exit Ticket

1. Solve each compound inequality for x and graph the solution on a number line.
   a. 9 + 2x < 17 and 7 - 4x < -9
   b. 6 ≤ x/2 ≤ 11
2. a. Give an example of a compound inequality separated by “or” that has a solution of all real number.
   b. Take the example from (a) and change the “or” to an “and.” Explain why the solution set is no longer all real numbers. Use a graph on a number line as part of your explanation.

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