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Published byAbel Baker Modified over 9 years ago
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An inequality is a statement that two quantities are not equal
An inequality is a statement that two quantities are not equal. The quantities are compared by using the following signs: ≤ A ≤ B A is less than or equal to B. < A < B than B. > A > B A is greater ≥ A ≥ B ≠ A ≠ B A is not A solution of an inequality is any value of the variable that makes the inequality true.
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Reading Math “No more than” means “less than or equal to.” “At least” means “greater than or equal to”.
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Turn on the AC when temperature is at least 85°F
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 is at least 85°F t ≥ 85 Draw a solid circle at 85. Shade all numbers greater than 85 and draw an arrow pointing to the right. t 85 75 80 85 90 70
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Solving one-step inequalities is much like solving one-step equations
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.
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Example 1A: Using Addition and Subtraction to Solve Inequalities
Solve the inequality and graph the solutions. x + 12 < 20 x + 12 < 20 Since 12 is added to x, subtract 12 from both sides to undo the addition. –12 –12 x + 0 < 8 x < 8 Draw an empty circle at 8. –10 –8 –6 –4 –2 2 4 6 8 10 Shade all numbers less than 8 and draw an arrow pointing to the left.
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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 Since 0.3 is subtracted from n, add 0.3 to both sides to undo the subtraction. 1.2 ≥ n – 0 1.2 ≥ n 1.2 Draw a solid circle at 1.2. 1 2 Shade all numbers less than 1.2 and draw an arrow pointing to the left.
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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. Understand the problem 1 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.
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Example 1C: Multiplying or Dividing by a Positive Number
Solve the inequality and graph the solutions. Since r is multiplied by , multiply both sides by the reciprocal of . r < 16 2 4 6 8 10 12 14 16 18 20
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Solve the inequality and graph the solutions.
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 5 –5 –10 –15 15
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Let p represent the number of tubes of paint that Jill can buy.
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 number of tubes is at most $20.00. 4.30 • p ≤ 20.00
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Lesson Quiz Solve each inequality and graph the solutions. 1. 8x < –24 x < –3 2. –5x ≥ 30 x ≤ –6 3. x > 20 4. x ≥ 6 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
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