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Main Idea

Key Concept: Properties of Inequality

Example 1: Solve Inequalities

Example 2: Solve Inequalities

Key Concept: Properties of Inequality

Example 3: Multiply by a Negative Number

Example 4: Divide by a Negative Number

Example 5: Real-World Example

• Solve and graph one-step inequalities by using the Multiplication or Division Properties of Inequality.

Solve Inequalities

Solve 6x < –30. Graph the solution set on a number line.

6x < –30 Write the inequality.

x < – 5 Simplify.

Draw an open dot at –5 with an arrow to the left.

Division Property of Inequality

Answer:

Solve 21 < 3n. Graph the solution set on a number line.

A. n < 7

B. n > 7

C. n < –7

D. n > –7

Solve Inequalities

Solve p ≥ 9. Graph the solution set on a

number line.

__12

Write the inequality.

Multiplication Property of Inequality

Simplify.

The solution is p ≥ 18. Graph the solution set.

Solve Inequalities

Answer:

Draw a closed dot at 18 with an arrow to the right.

Solve –2. Graph the solution set on a number line.

__k6

A. k ≤ 12

B. k ≤ –12

C. k ≥ 12

D. k ≥ –12

Multiply or Divide by a Negative Number

Solve the inequality ≤ 5. Graph the solution set on a number line.

__b–4

Write the inequality.

Multiplication Property of Inequality; reverse inequality symbol

Simplify.

Answer:

Solve > –3. Graph the solution set on a number line.

__h–6

A. h < 18

B. h > 18

C. h < –18

D. h > –18

Solve the inequality –4n > –60. Graph the solution set on a number line.

Multiply or Divide by a Negative Number

Write the inequality.

Division Property of Inequality; reverse inequality symbol

Simplify.

Answer:

Solve –8n 72. Graph the solution set on a number line.

A. n ≤ –9

B. n ≥ –9

C. n ≤ 9

D. n ≥ 9

BOOKS Jesse is filling a box with books that weigh 2 pounds each. The box can hold at most 15 pounds of books. Assuming that space is not an issue, write and solve an inequality to find how many books Jesse can put in the box.

The phrase at most means less than or equal to. Let p = the number of books in the box.

Write the inequality.

Division Property of Inequality

Simplify.

Answer: The solution is p ≤ 7.5. He can put at most 7 books in the box.

A. 5x ≤ 13; at most 2.6 pounds

B. 5x ≥ 13; at least 2.6 pounds

C. 13x ≤ 5; at most about 0.4 pound

D. 13x ≥ 5; at least about 0.4 pound

MONEY Victor has $13 to buy trail mix for a hiking trip. A pound of trail mix costs $5. Write and solve an inequality to find how many pounds of trail mix Victor can buy.