1. Warm Up Solve each equation. 1. –5a = 30 2. –6 –10 3. 4.
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. Solving an Inequality x < 8 Solve using addition:
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. Solving Using Subtraction
Subtract the same number from EACH side.

6. Using Subtraction…
Graph the solution.

7. 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.

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

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

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

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

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

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

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

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

18. Your Turn…. x + 3 > -4 x > -7 6d > 24 d > 4 2x - 8 < 14
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

19. Let p represent the number of tubes of paint that Jill can buy.
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.
$4.30
times
number of tubes
is at most
$20.00.
4.30 • p ≤
20.00

20. Example 3 Continued
4.30p ≤ 20.00
Since p is multiplied by 4.30, divide both sides by 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.

21. 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.
10 oz
times
number of servings
is at most
128 oz 10 • x ≤
128

22. Check It Out! Example 3 Continued
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.

23. Homework
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# odds
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