This document provides information on solving linear inequalities, including inequality symbols and keywords, steps to solve inequalities, and examples of applications with inequalities. To solve a linear inequality, use inverse operations to isolate the variable while maintaining the inequality sign, and flip the sign when multiplying or dividing by a negative number. An example shows solving the inequality 3 - 2x - 4 ≤ 18 to get the solution x ≥ -3.5. The document also gives an example of applying inequalities to determine the maximum amount friends can spend on concert tickets given their total budget and other expenses.
2. INEQUALITY SYMBOLS
LessThan < Open Circle Shade to the Left
LessThan or EqualTo < Closed Circle Shade to the Left
GreaterThan > Open Circle Shade to the Right
GreaterThan or EqualTo > Closed Circle Shade to the Right
3. KEYWORDS FORTHE INEQUALITY
LessThan:
■ Fewer than
■ Below
LessThan or EqualTo:
• No MoreThan
• Not Above
• Does Not Exceed
• At Most
GreaterThan or EqualTo:
• At least
• No fewer than
• No less than
GreaterThan:
• Above
• Exceeding
Click the link below for a few more examples on solving inequalities:
Introduction to Inequalities
4. TO SOLVEA LINEAR INEQUALITY:
■ Use inverse operations to isolate the variable
■ Do the same operation to both sides of the inequality
■ Flip the symbol when multiplying or dividing by a negative
Solve the inequality:
3 − 2 𝑥 − 4 ≤ 18
3 − 2𝑥 + 8 ≤ 18
11 − 2𝑥 ≤ 18
−2𝑥 ≤ 7
𝑥 ≥ −3.5
0-1-2-3-4-5
Click here to
watch a video
on Solving
Inequalities.
5. APPLICATIONSWITH INEQUALITIES
Sarah and her 2 closest friends have no more than $500 on their weekend trip. They plan to
purchase concert tickets for Friday night. They have spent $275 on the hotel. What is the
maximum amount they can spend on the concert tickets?
3𝑥 + 275 ≤ 500
3𝑥 ≤ 225
𝑥 ≤ 75
Sarah and her friends can spend no more than $75 on the tickets.