Embed Size (px)
Citation preview
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
>
<
>
<
<
>
WRITING INEQUALITIES
A number is greater than five.
x
Verbal expressions that suggest an inequality.
WRITING INEQUALITIES
A number is greater than five.
>x
Verbal expressions that suggest an inequality.
WRITING INEQUALITIES
A number is greater than five.
5
Writing equations #3
x >
Verbal expressions that suggest an inequality.
WRITING INEQUALITIES
A number is at least twelve.
x
Verbal expressions that suggest an inequality.
WRITING INEQUALITIES
A number is at least twelve.
>x
Verbal expressions that suggest an inequality.
WRITING INEQUALITIES
A number is at least twelve.
12
Writing equations #3
x >
Verbal expressions that suggest an inequality.
WRITING INEQUALITIES
Two less than a number is less than three.
Writing equations #3
– 2
Verbal expressions that suggest an inequality.
WRITING INEQUALITIES
Two less than a number is less than three.
Writing equations #3
– 2
Verbal expressions that suggest an inequality.
x
WRITING INEQUALITIES
Two less than a number is less than three.
Writing equations #3
– 2
Verbal expressions that suggest an inequality.
x <
WRITING INEQUALITIES
Two less than a number is less than three.
Writing equations #3
– 2
Verbal expressions that suggest an inequality.
x < 3
WRITING INEQUALITIES
TRY THESE
Writing equations #3
Verbal expressions that suggest an inequality.
The sum of eight and a number is at least six.
8 + x > 6
WRITING INEQUALITIES
TRY THESE
Writing equations #3
Verbal expressions that suggest an inequality.
The product of seven and a number is less than or equal to three less than twice the number.
7x < 2x - 3
SOLVING INEQUALITIESUsing Addition and Subtraction
ADDITION PROPERTY OF INEQUALITY
For any numbers a, b, and c,if a > b, then a + c > b + c
25 > 2025 + 5 > 20 + 5
30 > 25
Addition Property of Equality
SOLVING INEQUALITIESUsing Addition and Subtraction
SAMPLE PROBLEMS
Solve & Graph: x – 3 > 7+3 +3
x > 10
Check: 10 – 3 = 7 True
Solving Equations (Sample 1)
Check 2: 11 – 3 > 7 True
0 10
SAMPLE PROBLEMS
Solve & Graph: x + 6 < 2-6 -6
x < - 4
Check: - 4 + 6 = 2 True
Solving Equations (Sample 2)
SOLVING INEQUALITIESUsing Addition and Subtraction
Check 2: - 5 + 6 < 2 True
- 4 0
SAMPLE PROBLEMS
Solve & Graph: 11 + x > - 5-11 -11
x > - 16
Check: 11 + (-16) = - 5 True
Check 2: 11 + (-15) > - 5 True
SOLVING INEQUALITIESUsing Addition and Subtraction
-16 0
SAMPLE PROBLEMS
Solve: 55 – x > 70-55 -55
-x > 15
Check: 55 – (-15) = 70 True
x > -15
Change signsNOTE: sign stays with x
Solving Equations (Sample 4)
Check 2: 55 – (-14) > 70 False…WHY?
SOLVING INEQUALITIESUsing Addition and Subtraction
SOLVING INEQUALITIESUsing Multiplication and Division
MULTIPLICATION PROPERTY OF INEQUALITY
For any numbers a, b, and c > 0,if a > b, then ac > bc
25 > 2025(5) > 20(5)
125 > 100
Addition Property of Equality
SOLVING INEQUALITIESUsing Multiplication and Division
MULTIPLICATION PROPERTY OF INEQUALITY
For any numbers a, b, and c < 0,if a > b, then ac < bc
25 > 2025(-2) > 20(-2)
-50
Addition Property of Equality
> -40 Ding!!
Just like solving equations, except……when multiplying or dividing by a negative.
SOLVE: -3x > 6
x < -2
-3 -3 Ding!!
SOLVING INEQUALITIESUsing Multiplication and Division
Just like solving equations, except……when multiplying or dividing by a negative.
SOLVE:
x < 12
(-2) (-2) Ding!!
SOLVING INEQUALITIESUsing Multiplication and Division
62
x
SOLVE: 3x – 12 > 5x + 4
-2x – 12 > 4
-2x > 16
x -8>< Ding!!
SOLVING INEQUALITIESUsing Multiplication and Division
Just like solving equations, except……when multiplying or dividing by a negative.
-5x -5x
+12 +12
-2 -2
