1 / 23

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.

jsiler
Download Presentation

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

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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

More Related