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Warm Up Solve each equation. 1. –5 a = 30 2.

Warm Up Solve each equation. 1. –5 a = 30 2. –10. –6. 4. 3. Graph each inequality. 5. x ≥ –10. 6. x < –3. Solving and Graphing Inequalities. Symbols. Less than. Greater than. Less than OR EQUAL TO. Greater than OR EQUAL TO. +3 +3. Solving an Inequality.

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Warm Up Solve each equation. 1. –5 a = 30 2.

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  1. Warm Up Solve each equation. 1. –5a = 30 2. –10 –6 4. 3. Graph each inequality. 5. x ≥ –10 6.x < –3

  2. Solving and Graphing Inequalities

  3. Symbols Less than Greater than Less than OR EQUAL TO Greater than OR EQUAL TO

  4. +3 +3 Solving an Inequality Solving a linear inequality in one variable is much like solving a linear equation in one variable. Isolate the variable on one side using inverse operations. Solve using addition: x – 3 < 5 Add the same number to EACH side. x < 8

  5. -6 -6 Solving Using Subtraction Subtract the same number from EACH side.

  6. -5 -4 -3 -2 -1 0 1 2 3 4 5 Using Subtraction… Graph the solution.

  7. -5 -4 -3 -2 -1 0 1 2 3 4 5 Using Addition… Graph the solution.

  8. THE TRAP….. When you multiply or divide each side of an inequality by a negative number, you must reverse the inequality symbol to maintain a true statement.

  9. 3 3 Solving Using Division Divide each side by the same positive number.

  10. (-1) (-1) See the switch Solving by multiplication of a negative # Multiply each side by the same negative number and REVERSE the inequality symbol. Multiply by (-1).

  11. (2) (2) Solving using Multiplication Multiply each side by the same positive number.

  12. -2 -2 Solving by dividing by a negative # Divide each side by the same negative number and reverse the inequality symbol.

  13. -25 -20 -15 -10 -5 0 5 10 15 20 25 Solve an Inequality w + 5 < 8 - 5 -5 w < 3 All numbers less than 3 are solutions to this problem!

  14. -25 -20 -15 -10 -5 0 5 10 15 20 25 More Examples 8 + r ≥ -2 -8 -8 r -10 All numbers greater than-10 (including -10) ≥

  15. -25 -20 -15 -10 -5 0 5 10 15 20 25 More Examples 2x > -2 2 2 x > -1 All numbers greater than -1 make this problem true!

  16. -25 -20 -15 -10 -5 0 5 10 15 20 25 More Examples 2h + 8 ≤ 24 -8 -8 2h ≤ 16 2 2 h ≤ 8 All numbers less than 8 (including 8)

  17. Your Turn…. • Solve the inequality and graph the answer. • x + 3 > -4 • 6d > 24 • 2x - 8 < 14 • -2c – 4 < 2 • x > -7 • d > 4 • x < 11 • c < -3

  18. number of tubes is at most times $4.30 $20.00. 20.00 4.30 ≤ p • 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.

  19. Example 3 Continued 4.30p ≤ 20.00 Since p is multiplied by 4.30, divide both sides by 4.30. The symbol does not change. p ≤ 4.65… Since Jill can buy only whole numbers of tubes, she can buy 0, 1, 2, 3, or 4 tubes of paint.

  20. number of servings is at most times 128 oz 10 oz 128 10 ≤ x • Check It Out! Example 3 A pitcher holds 128 ounces of juice. What are the possible numbers of 10-ounce servings that one pitcher can fill? Let x represent the number of servings of juice the pitcher can contain.

  21. Check It Out! Example 3 Continued 10x ≤ 128 Since x is multiplied by 10, divide both sides by 10. The symbol does not change. x ≤ 12.8 The pitcher can fill 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, or 12 servings.

  22. Homework Page 584 # 1-19 odds 1-10 Castle Learning

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