Algebra 2 Lesson 1-4 (Page 26)

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Presentation transcript:

Algebra 2 Lesson 1-4 (Page 26) Solving Inequalities ALGEBRA 2 LESSON 1-4 Algebra 2 Lesson 1-4 (Page 26) 1-1

Properties of Inequalities (Page 26) Solving Inequalities ALGEBRA 2 LESSON 1-4 Properties of Inequalities (Page 26) 1-1

To solve and graph inequalities. Solving Inequalities ALGEBRA 2 LESSON 1-4 7 To solve and graph inequalities. 1-1

Solving and Graphing Inequalities Solving Inequalities ALGEBRA 2 LESSON 1-4 Solving and Graphing Inequalities 7 Solve –2x < 3(x – 5). Graph the solution. –2x < 3(x – 5) –2x < 3x – 15 Distributive Property –5x < –15 Subtract 3x from both sides. x > 3 Divide each side by –5 and reverse the inequality. 1-4

Solving and Graphing Inequalities Solving Inequalities ALGEBRA 2 LESSON 1-4 Solving and Graphing Inequalities 7 Solve the inequality. Graph the solution. 1-3

Solving and Graphing Inequalities Solving Inequalities ALGEBRA 2 LESSON 1-4 Solving and Graphing Inequalities 7 Solve the inequality. Graph the solution. 1-3

No Solutions or All Real Numbers as Solutions Solving Inequalities ALGEBRA 2 LESSON 1-4 No Solutions or All Real Numbers as Solutions 7 Solve 7x 7(2 + x). Graph the solution. > – 7x 7(2 + x) > – 7x 14 + 7x Distributive Property > – 0 14 Subtract 7x from both sides. > – The last inequality is always false, so 7x 7(2 + x) is always false. It has no solution. > – 1-4

No Solutions or All Real Numbers as Solutions Solving Inequalities ALGEBRA 2 LESSON 1-4 No Solutions or All Real Numbers as Solutions 7 Solve the inequality. Graph the solution. 1-3

No Solutions or All Real Numbers as Solutions Solving Inequalities ALGEBRA 2 LESSON 1-4 No Solutions or All Real Numbers as Solutions 7 Solve the inequality. Graph the solution. 1-3

HOT 7 Solving Inequalities ALGEBRA 2 LESSON 1-4 HOT 7 A real estate agent earns a salary of $2000 per month plus 4% of the sales. What must the sales be if the salesperson is to have a monthly income of at least $5000? Relate: $2000 + 4% of sales $5000 > – Define: Let x = sales (in dollars). Write: 2000 + 0.04x 5000 > – 0.04x 3000 Subtract 2000 from each side. > – x 75,000 Divide each side by 0.04. > – The sales must be greater than or equal to $75,000. 1-4

HOT 7 Solving Inequalities ALGEBRA 2 LESSON 1-4 HOT 7 A salesperson earns a salary of $700 per month plus 2% of the sales. What must the sales be if the salesperson is to have a Monthly income of at least $1800? 1-3

To solve and write compound inequalities. Solving Inequalities ALGEBRA 2 LESSON 1-4 8 To solve and write compound inequalities. 1-1

A compound inequality is a pair of Inequalities joined by and or or. Solving Inequalities ALGEBRA 2 LESSON 1-4 New Vocabulary A compound inequality is a pair of Inequalities joined by and or or. 1-1

Solving Inequalities ALGEBRA 2 LESSON 1-4 8 Graph the solution of 2x – 1 3x and x > 4x – 9. < – 2x – 1 3x and x > 4x – 9 < – –1 x 9 > 3x < – –1 x and 3 > x < – This compound inequality can be written as –1 x < 3. < – 1-4

Solving Inequalities ALGEBRA 2 LESSON 1-4 8 Graph the solution of 2x – 1 3x and x > 4x – 9. < – 1-4

Solving Inequalities ALGEBRA 2 LESSON 1-4 8 Graph the solution of 1-3

Solving Inequalities ALGEBRA 2 LESSON 1-4 8 Graph the solution of 3x + 9 < –3 or –2x + 1 < 5. 3x + 9 < –3 or –2x + 1 < 5 3x < –12 –2x < 4 x < –4 or x > –2 1-4

Solving Inequalities ALGEBRA 2 LESSON 1-4 8 Graph the solution of 3x + 9 < –3 or –2x + 1 < 5. 1-4

Solving Inequalities ALGEBRA 2 LESSON 1-4 8 Solve the compound inequality and graph the solution. 1-3

Solving Inequalities ALGEBRA 2 LESSON 1-4 8 Solve the compound inequality and graph the solution. 1-3

HOT 8 Solving Inequalities ALGEBRA 2 LESSON 1-4 HOT 8 A strip of wood is to be 17 cm long with a tolerance of ± 0.15 cm. How much should be trimmed from a strip 18 cm long to allow it to meet specifications? Relate: minimum length final length maximum length Define: Let x = number of centimeters to remove. < – Write: 17 – 0.15 18 – x 17 + 0.15 < – 16.85 18 – x 17.15 Simplify. < – –1.15 – x –0.85 Subtract 18. < – 1.15 x 0.85 Multiply by –1. > – At least 0.85 cm and no more than 1.15 cm should be trimmed off to meet specifications. 1-4

HOT 8 Solving Inequalities ALGEBRA 2 LESSON 1-4 HOT 8 The plans for a circular plastic part in an insulin pump require A diameter of 1.5in. with a tolerance of +0.2in. A machinist finds that the diameter is now 1.73in. By how much should the machinist decrease the diameter. 1-3