Solve Inequalities and Graph Solutions on a Number Line

1. Transparency 5 Click the mouse button or press the Space Bar to display the answers.

2. Splash Screen

3. Example 5-7c Objective Solve inequalities

4. Example 5-7c Vocabulary Inequality A mathematical sentence that contains the < , >, <, or > symbols

5. Example 5-7c Math Symbols < is less than > is greater than < is less than or equal to > Is greater than or equal to

6. Lesson 5 Contents Example 1Graph Solutions of Inequalities Example 2Graph Solutions of Inequalities Example 3Graph Solutions of Inequalities Example 4Graph Solutions of Inequalities Example 5Solve One-Step Inequalities Example 6Solve One-Step Inequalities

7. Graph the inequality on a number line. Example 5-1a Write the inequality Draw an appropriate number line Put a circle on the starting number 1/6

8. Graph the inequality on a number line. The open circle means that the number is not included in the solution. Example 5-1a Determine the direction of the line by looking at the sign with the number Begin at the number and draw the line “less than” 2 NOTE: The arrow is going the same direction as the sign! Answer: 1/6

9. Graph the inequality on a number line. Example 5-1b Answer: 1/6

10. Graph the inequality on a number line. Example 5-2a Write the inequality Draw an appropriate number line Put a circle on the starting number 2/6

11. Graph the inequality on a number line. The closed circle means that the number is included in the solution. Example 5-2a Determine the direction of the line by looking at the sign with the number Begin at the number and draw the line “greater than” -1 Since the sign is “greater than OR equal to” fill in the circle Answer: 2/6

12. Graph the inequality on a number line. Example 5-2b Answer: 2/6

13. Graph the inequality on a number line. Example 5-3a Write the inequality Draw an appropriate number line Put a circle on the starting number 3/6

14. Graph the inequality on a number line. The open circle means that the number is not included in the solution. Example 5-3a Determine the direction of the line by looking at the sign with the number Begin at the number and draw the line “greater than” -3 NOTE: The arrow is going the same direction as the sign! Answer: 3/6

15. Graph the inequality on a number line. Example 5-3b Answer: 3/6

16. Graph the inequality on a number line. Example 5-4a Write the inequality Draw an appropriate number line Put a circle on the starting number 4/6

17. Graph the inequality on a number line. The closed circle means that the number is included in the solution. Example 5-4a Determine the direction of the line by looking at the sign with the number Begin at the number and draw the line “less than” 0 Since the sign is “less than OR equal to” fill in the circle Answer: 4/6

18. Graph the inequality on a number line. Example 5-4b Answer: 4/6

19. Solve Then graph the solution. Example 5-5a Write the inequality. Ask “what is being done to the variable ?” The variable is being subtracted by 7 Do the inverse operation on each side of the equal sign 5/6

20. Solve Then graph the solution. Example 5-5a Bring down x - 7 x – 7 + 7 x – 7 x – 7 + 7 < 2 x – 7 + 7 < 2 + 7 Add 7 x x + 0 < 9 x + 0 x + 0 < Bring down < 2 Add 7 Bring down x Combine “like” terms Bring down < Combine “like” terms 5/6

21. Solve Then graph the solution. Example 5-5a Use the Identity Property to add x + 0 x – 7 + 7 x – 7 x – 7 + 7 < 2 + 7 x – 7 + 7 < 2 Bring down < 9 x x + 0 x + 0 < x + 0 < 9 Graph the solution x x < 9 Draw an appropriate number line 5/6

22. Solve Then graph the solution. Example 5-5a Put a circle on the starting number x – 7 + 7 x – 7 x – 7 + 7 < 2 x – 7 + 7 < 2 + 7 Determine the direction of the line by looking at the sign with the number x x + 0 < 9 x + 0 x + 0 < Begin at the number and draw the line “less than” 9 x x < 9 Answer: x < 9 5/6

23. Solve Then graph the solution. Example 5-5b Answer: 6/6

24. Solve Graph the solution. Example 5-6a Write the inequality. Ask “what is being done to the variable ?” The variable is being multiplied by 6 Do the inverse operation on each side of the equal sign 6/6

25. Solve Graph the solution. Example 5-6a Bring down 6x > 24 Using the fraction bar, divide 6x by 6 Divide 24 by 6 Combine “like” terms 1  x 1  x > 1  x > 4 Bring down > Combine “like” terms Use the Identity Property to multiply 1  x Bring down > 4 6/6

26. Example 5-6a Graph the solution Draw an appropriate number line Put a circle on the starting number Determine the direction of the line by looking at the sign with the number Begin at the number and draw the line “greater than” 4 6/6

27. Example 5-6a Since the sign is “greater than OR equal to” fill in the circle Answer: 6/6

28. Solve Graph the solution. Example 5-6b Answer: 6/6

29. End of Lesson 5 Assignment

30. Example 5-7a BASEBALL CARDS Jacob is buying uncirculated baseball cards online. The cards he has chosen are $6.70 each and the Web site charges a $1.50 service charge for each sale. If Jacob has no more than $35 to spend, how many cards can he buy? Let c represent the number of baseball cards Jacob can buy. Write the equation. Ask “what is being done to the variable first ?” c is being added by 1.50 7/7

31. Example 5-7b Do the inverse operation on each side 6.70c + 1.50 - 1.50 < 35.00 - 1.50 Simplify 6.70c + 0 < 33.50 Ask “what is being done to the variable second?” 6.70c < 33.50 c is being multiplied by 6.70 Do the inverse operation on each side 7/7

32. Example 5-7b Simplify 1c < 5 Answer: Jacob can buy no more than 5 baseball cards. 7/7

33. Example 5-7c * BOWLING Danielle is going bowling. The charge for renting shoes is $1.25 and each game costs $2.25. If Danielle has no more than $8 to spend on bowling, how many games can she play? Answer: no more than 3 7/7