This document discusses the properties of inequalities and how to solve one-step inequalities. It explains that the same rules apply as when solving equations, except when multiplying or dividing by a negative number, the inequality symbol must be reversed. The document provides examples of solving various one-step inequalities and graphing their solutions. It also includes practice problems for the reader to solve.

1. 3-2/3-3 Solving One-Step
Inequalities

2. Properties of Inequalities
• Addition Property:
• If you add the same number to both
sides of an inequality, it remains true.

3. • Subtraction Property:
• If you subtract the same number from
both sides of an inequality, it remains
true.

4. • Multiplication/Division Property
(Case 1):
• If you multiply/divide both sides of an
inequality by the same positive number, it
remains true.

5. • Multiplication/Division Property
(Case 2):
• If you multiply/divide both sides of an
inequality by the same negative number,
the inequality
symbol must
be reversed to
remain true.

6. Solving One-Step Inequalities
• Just like solving equations!
• Do opposite operations to get variable
alone.
• BE CAREFUL!
▫ If you multiply or divide by a negative
number, you must reverse the inequality
symbol!

7. Example 1
• Solve x – 6 ≥ 10. Graph the solution.

8. You Try!
• Solve b – 2 > -9. Graph the solution.

9. Example 2
• Solve -8 > 1.4 + x. Graph the solution.

10. You Try!
• Solve k + 5 ≤ -3. Graph the solution.

11. Example 3
• Solve
. Graph the solution.

12. You Try!
• Solve 3x ≤ 24. Graph the solution.

13. Example 4
• Solve -7y ≤ -35. Graph the solution.

14. You Try!
• Solve
. Graph the solution.