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Solving Inequalities

Solving Inequalities. Section 1.4. Check Skills You’ll Need. Work problems 1-8 on page 26 in your textbook. Answers:. In this lesson you will. Solve and graph inequalities Solve and write compound inequalities. Solving and Graphing Inequalities. Solve -2x < 3(x – 5). Graph the solution.

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Solving Inequalities

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  1. Solving Inequalities Section 1.4

  2. Check Skills You’ll Need • Work problems 1-8 on page 26 in your textbook. • Answers:

  3. In this lesson you will • Solve and graph inequalities • Solve and write compound inequalities

  4. Solving and Graphing Inequalities • Solve -2x < 3(x – 5). Graph the solution.

  5. Check Understanding • Solve each inequality and graph the solution.

  6. Example 2 • Solve 7x ≥ 7(2 + x)

  7. Check Understanding • Solve each inequality and graph the solution.

  8. Inequalities with No Solution or All Real Numbers as Solutions • If an inequality is always false, it has no solution. 0 < -7 • If an inequality is always true, then all real numbers are solutions. 3 > 0

  9. -2 -1 0 1 2 Check Understanding All real numbers are solutions.

  10. Check Understanding This inequality has no solution.

  11. -1 3 Compound Inequalities • Graph the solution of 2x – 1 ≤ 3x and x > 4x – 9.

  12. Check Understanding • Graph the solution of the compound inequality 6 9

  13. Compound Inequalities Containing OR • Graph the solution of 3x + 9 < -3 or -2x + 1 < 5 -4 -2

  14. Check Understanding • Solve the compound inequality and graph the solution. 4 5

  15. Applying Compound Inequalities • 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? Mimimum length ≤ Final length ≤ Maximum length Let x be the number of centimeters to remove. 16.85 16.85 16.85 ≤ ≤ ≤ 18 - x 18 - x 18 - x ≤ ≤ ≤ 17.15 17.15 17.15 Now solve for x.

  16. 16.85 ≤ 18 - x ≤ 17.15 Subtract 18 Multiply by -1 At least .85 cm and no more than 1.15 cm should be trimmed.

  17. Mimimum diameter ≤ Final length ≤ Maximum diameter Check Understanding • Now work the problem on page 29 of your textbook. Let x be the number of inches to remove The diameter should be decreased by at least 0.03 in and no more than 0.43 in.

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