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2-1 Graphing and Writing Inequalities An inequality is a statement that two quantities are not equal. The quantities are compared by using the following signs: ≥ ≠ A≤B A≥B A≠B A is less than or equal to B. A is greater than or equal to B. A is not equal to B. < > ≤ A<B A>B A is less than B. A is greater than 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 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: Application Ray’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. Let t represent the temperatures at which Ray can turn on the air conditioner. Turn on the AC when temperature t ≥ t 85 70 75 80 Holt McDougal Algebra 1 85 is at least 85°F 90 85 Draw a solid circle at 85. Shade all numbers greater than 85 and draw an arrow pointing to the right. 2-1 Graphing and Writing Inequalities Solving one-step inequalities is much like solving one-step equations. To solve an inequality, you need to isolate the variable using the properties of inequality and inverse operations. Holt McDougal Algebra 1 2-1 Graphing and Writing Inequalities Example 1A: Using Addition and Subtraction to Solve Inequalities Solve the inequality and graph the solutions. x + 12 < 20 x + 12 < 20 –12 –12 x+0 < 8 x < 8 –10 –8 –6 –4 –2 0 Holt McDougal Algebra 1 2 Since 12 is added to x, subtract 12 from both sides to undo the addition. 4 6 8 10 Draw an empty circle at 8. Shade all numbers less than 8 and draw an arrow pointing to the left. 2-1 Graphing and Writing Inequalities Example 1C: Using Addition and Subtraction to Solve Inequalities Solve the inequality and graph the solutions. 0.9 ≥ n – 0.3 0.9 ≥ n – 0.3 +0.3 +0.3 1.2 ≥ n – 0 1.2 ≥ n Since 0.3 is subtracted from n, add 0.3 to both sides to undo the subtraction. 1.2 0 1 Holt McDougal Algebra 1 2 Draw a solid circle at 1.2. Shade all numbers less than 1.2 and draw an arrow pointing to the left. 2-1 Graphing and Writing Inequalities Example 2: 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. 1 Understand the problem The answer will be an inequality and a graph that show all the possible amounts of money that Sami can spend. List important information: • Sami can spend up to, or at most $30. • Sami has already spent $14. Holt McDougal Algebra 1 2-1 Graphing and Writing Inequalities Example 1C: Multiplying or Dividing by a Positive Number Solve the inequality and graph the solutions. r < 16 0 2 4 6 Since r is multiplied by , multiply both sides by the reciprocal of . 8 10 12 14 16 18 20 Holt McDougal Algebra 1 2-1 Graphing and Writing Inequalities Check It Out! Example 1b Solve the inequality and graph the solutions. –50 ≥ 5q Since q is multiplied by 5, divide both sides by 5. –10 ≥ q –15 –10 –5 Holt McDougal Algebra 1 0 5 15 2-1 Graphing and Writing Inequalities Example 3: Application Jill has a $20 gift card to an art supply store where 4 oz tubes of paint are $4.30 each after tax. What are the possible numbers of tubes that Jill can buy? Let p represent the number of tubes of paint that Jill can buy. $4.30 times 4.30 • Holt McDougal Algebra 1 number of tubes is at most $20.00. p ≤ 20.00 2-1 Graphing and Writing Inequalities Lesson Quiz Solve each inequality and graph the solutions. 1. 8x < –24 x < –3 2. –5x ≥ 30 x ≤ –6 3. 4. x≥6 x > 20 5. A soccer coach plans to order more shirts for her team. Each shirt costs $9.85. She has $77 left in her uniform budget. What are the possible number of shirts she can buy? 0, 1, 2, 3, 4, 5, 6, or 7 shirts Holt McDougal Algebra 1