1. Verbal Expressions for =
WRITING INEQUALITIES
Verbal expressions that suggest an inequality.
>
IS MORE THAN
<
IS LESS THAN
>
IS AT LEAST
<
IS AT MOST
<
IS LESS THAN OR EQUAL TO
>
IS GREATER THAN OR EQUAL TO
Verbal Expressions for =

2. x Writing equations #1 Verbal expressions that suggest an inequality.
WRITING INEQUALITIES
Verbal expressions that suggest an inequality.
A number is greater than five. x
Writing equations #1

3. x > Writing equations #2
WRITING INEQUALITIES
Verbal expressions that suggest an inequality.
A number is greater than five. x
>
Writing equations #2

4. x > 5 Writing equations #3
WRITING INEQUALITIES
Verbal expressions that suggest an inequality.
A number is greater than five. x
> 5
Writing equations #3

5. x Writing equations #1 Verbal expressions that suggest an inequality.
WRITING INEQUALITIES
Verbal expressions that suggest an inequality.
A number is at least twelve. x
Writing equations #1

6. x > Writing equations #2
WRITING INEQUALITIES
Verbal expressions that suggest an inequality.
A number is at least twelve. x
>
Writing equations #2

7. x > 12 Writing equations #3
WRITING INEQUALITIES
Verbal expressions that suggest an inequality.
A number is at least twelve. x
> 12
Writing equations #3

8. WRITING INEQUALITIES
Verbal expressions that suggest an inequality.
Two less than a number is less than three.
– 2
Writing equations #3

9. WRITING INEQUALITIES
Verbal expressions that suggest an inequality.
Two less than a number is less than three. x
– 2
Writing equations #3

10. x – 2 < Writing equations #3
WRITING INEQUALITIES
Verbal expressions that suggest an inequality.
Two less than a number is less than three. x
– 2
<
Writing equations #3

11. x – 2 < 3 Writing equations #3
WRITING INEQUALITIES
Verbal expressions that suggest an inequality.
Two less than a number is less than three. x
– 2
< 3
Writing equations #3

12. 8 + x > 6 Writing equations #3
WRITING INEQUALITIES
Verbal expressions that suggest an inequality.
TRY THESE
The sum of eight and a number is at least six.
8 + x > 6
Writing equations #3

13. Verbal expressions that suggest an inequality.
WRITING INEQUALITIES
Verbal expressions that suggest an inequality.
TRY THESE
The product of seven and a number is less than or equal to three less than twice the number.
7x < 2x - 3
Writing equations #3

14. Addition Property of Equality
SOLVING INEQUALITIES
Using Addition and Subtraction
ADDITION PROPERTY OF INEQUALITY
For any numbers a, b, and c,
if a > b, then a + c > b + c
25 > 20
>
30 > 25
Addition Property of Equality

15. Solving Equations (Sample 1)
SOLVING INEQUALITIES
Using Addition and Subtraction
SAMPLE PROBLEMS
Solve & Graph: x – 3 > 7
x > 10
Check: 10 – 3 = 7 True
Check 2: 11 – 3 > 7 True 10
Solving Equations (Sample 1)

16. Solving Equations (Sample 2)
SOLVING INEQUALITIES
Using Addition and Subtraction
SAMPLE PROBLEMS
Solve & Graph: x + 6 < 2
x < - 4
Check: = 2 True
Check 2: < 2 True
- 4
Solving Equations (Sample 2)

17. Solving Equations (Sample 3)
SOLVING INEQUALITIES
Using Addition and Subtraction
SAMPLE PROBLEMS
Solve & Graph: x > - 5
x > - 16
Check: (-16) = True
Check 2: (-15) > True
-16
Solving Equations (Sample 3)

18. Solving Equations (Sample 4)
SOLVING INEQUALITIES
Using Addition and Subtraction
SAMPLE PROBLEMS
Solve: 55 – x > 70
-x > 15
NOTE: sign stays with x 
Change signs
x > -15
Check: 55 – (-15) = 70 True
Check 2: 55 – (-14) > 70 False… WHY?
Solving Equations (Sample 4)

19. Addition Property of Equality
SOLVING INEQUALITIES
Using Multiplication and Division
MULTIPLICATION PROPERTY OF INEQUALITY
For any numbers a, b, and c > 0,
if a > b, then ac > bc
25 > 20
25(5) > 20(5)
125 > 100
Addition Property of Equality

20. Addition Property of Equality
SOLVING INEQUALITIES
Using Multiplication and Division
MULTIPLICATION PROPERTY OF INEQUALITY
For any numbers a, b, and c < 0,
if a > b, then ac < bc
25 > 20
25(-2) > 20(-2)
-50
>
-40
Ding!!
Addition Property of Equality

21. Using Multiplication and Division
SOLVING INEQUALITIES
Using Multiplication and Division
Just like solving equations, except…
…when multiplying or dividing by a negative.
SOLVE: -3x > 6
Ding!!
x < -2

22. Using Multiplication and Division
SOLVING INEQUALITIES
Using Multiplication and Division
Just like solving equations, except…
…when multiplying or dividing by a negative.
SOLVE:
(-2) (-2)
Ding!!
x < 12

23. Using Multiplication and Division
SOLVING INEQUALITIES
Using Multiplication and Division
Just like solving equations, except…
…when multiplying or dividing by a negative.
SOLVE: 3x – 12 > 5x + 4
-5x x
-2x – 12 > 4
-2x > 16 x
<
>
Ding!!