Holt McDougal Algebra 1

2-1 Graphing and Writing Inequalities

Warm UpCompare. Write <, >, or =. 1. –3 2 3.

2. 6.5 6.3 < >

> 4. 0.25 =

Tell whether the inequality x < 5 is true or false for the following values of x.

5. x = –10 T 6. x = 5 F

7. x = 4.99 T 8. x = T

Holt McDougal Algebra 1

2-1 Graphing and Writing Inequalities

An inequality is a statement that two quantities are not necessarily equal. The quantities are compared by using the following signs:

≤A ≤ B

<A < B

>A > B

≥A ≥ B

≠A ≠ B

A solution of an inequality is any value of the variable that makes the inequality true.

Holt McDougal Algebra 1

2-1 Graphing and Writing Inequalities

Holt McDougal Algebra 1

2-1 Graphing and Writing Inequalities

Example 1: Graphing Inequalities

Graph each inequality.

A. m ≥

B. t < 5(–1 + 3)

Holt McDougal Algebra 1

2-1 Graphing and Writing Inequalities

Example 2: Writing an Inequality from a Graph

Write the inequality shown by each graph.

Holt McDougal Algebra 1

2-1 Graphing and Writing Inequalities

Reading Math

“No more than” means “less than or equal to.”

“At least” means “greater than or equal to”.

Holt McDougal Algebra 1

2-1 Graphing and Writing Inequalities

Example 4: ApplicationRay’s dad told him not to turn on the air conditioner unless the temperature is at least 85°F. Define a variable and write an inequality for the temperatures at which Ray can turn on the air conditioner. Graph the solutions.

Holt McDougal Algebra 1

2-1 Graphing and Writing Inequalities

A store’s employees earn at least $8.50 per hour. Define a variable and write an inequality for the amount the employees may earn per hour. Graph the solutions.

Check It Out! Example 4

Holt McDougal Algebra 1

2-1 Graphing and Writing Inequalities

Example 5: Using Addition and Subtraction to SolveInequalities

Solve the inequality and graph the solutions.

a) x + 12 < 20 b) d – 5 > –7

c) 0.9 ≥ n – 0.3

Holt McDougal Algebra 1

2-1 Graphing and Writing Inequalities

Example 6: Problem-Solving Application

Sami has a gift card. She has already used $14 of the total value, which was $30. Write, solve, and graph an inequality to show how much more she can spend.

Holt McDougal Algebra 1

2-1 Graphing and Writing Inequalities

Check It Out! Example 6

The Recommended Daily Allowance (RDA) of iron for a female in Sarah’s age group (14-18 years) is 15 mg per day. Sarah has consumed 11 mg of iron today. Write and solve an inequality to show how many more milligrams of iron Sarah can consume without exceeding RDA.

Holt McDougal Algebra 1

2-1 Graphing and Writing Inequalities

Mrs. Lawrence wants to buy an antique bracelet at an auction. She is willing to bid no more than $550. So far, the highest bid is $475. Write and solve an inequality to determine the amount Mrs. Lawrence can add to the bid. Check your answer.

Example 7: Application

Holt McDougal Algebra 1

2-1 Graphing and Writing Inequalities

Check It Out! Example 7

Josh wants to try to break the school bench press record of 282 pounds. He currently can bench press 250 pounds. Write and solve an inequality to determine how many more pounds Josh needs to lift to break the school record. Check your answer.

Holt McDougal Algebra 1

2-1 Graphing and Writing Inequalities

Homework: Page 103 #26-37; Page 109 #7-15, 16-

22 even, 25, 31, 34-37