A1.1.3.1 - Write, solve, and/or graph linear inequalities using various methods.

Key Vocabulary: Compound Inequality, Linear Inequality

A1.1.3.1.1 - Write or solve compound inequalities and/or graph their solution sets on a number line (may include absolute value inequalities).


A compound inequality is shown below.
5 < 2 – 3y < 14
What is the solution of the compound inequality?

A. -4 > y> -1
B. –4 < y < –1
C. 1 > y > 4
D. 1 < y < 4

Answer: B

A1.1.3.1.2 - Identify or graph the solution set to a linear inequality on a number line.


The solution set of an inequality is graphed on the number line below.
The graph shows the solution set of which inequality?

A.2x + 5 < –1
B. 2x + 5 ≤ –1
C. 2x + 5 > –1
D. 2x + 5 ≥ –1

Answer: D

A1.1.3.1.3 - Interpret solutions to problems in the context of the problem situation. Note: Limit to linear inequalities.


A baseball team had $1,000 to spend on supplies. The team spent $185 on a new bat. New baseballs cost $4 each. The inequality 185 + 4b ≤ 1,000 can be used to determine the number of new baseballs (b) that the team can purchase. Which statement about the number of new baseballs that can be purchased is true?

A.The team can purchase 204 new baseballs.
B. The minimum number of new baseballs that can be purchased is 185.
C. The maximum number of new baseballs that can be purchased is 185.
D. The team can purchase 185 new baseballs, but this number is neither the maximum nor the minimum.

Answer: D

Additional Resources:

Khan Academy Videos - Compound Inequalities
Khan Academy Videos - Graphing and solving linear inequalities