Download Solving Inequalities

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
Verbal expressions that suggest
an inequality.
A number is greater than five.
x
WRITING INEQUALITIES
Verbal expressions that suggest
an inequality.
A number is greater than five.
x
>
WRITING INEQUALITIES
Verbal expressions that suggest
an inequality.
A number is greater than five.
x
>
5
WRITING INEQUALITIES
Verbal expressions that suggest
an inequality.
A number is at least twelve.
x
WRITING INEQUALITIES
Verbal expressions that suggest
an inequality.
A number is at least twelve.
x
>
WRITING INEQUALITIES
Verbal expressions that suggest
an inequality.
A number is at least twelve.
x
>
12
WRITING INEQUALITIES
Verbal expressions that suggest
an inequality.
Two less than a number is less than three.
–2
WRITING INEQUALITIES
Verbal expressions that suggest
an inequality.
Two less than a number is less than three.
x –2
WRITING INEQUALITIES
Verbal expressions that suggest
an inequality.
Two less than a number is less than three.
x –2
<
WRITING INEQUALITIES
Verbal expressions that suggest
an inequality.
Two less than a number is less than three.
x –2
< 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 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
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
25 + 5 > 20 + 5
30 > 25
SOLVING INEQUALITIES
Using Addition and Subtraction
SAMPLE PROBLEMS
Solve & Graph: x – 3 > 7
+3
+3
x > 10
Check: 10 – 3 = 7 True
Check 2: 11 – 3 > 7 True
0
10
SOLVING INEQUALITIES
Using Addition and Subtraction
SAMPLE PROBLEMS
Solve & Graph: x + 6 < 2
-6
-6
x < -4
Check: -4 + 6 = 2 True
Check 2: -5 + 6 < 2 True
-4
0
SOLVING INEQUALITIES
Using Addition and Subtraction
SAMPLE PROBLEMS
Solve & Graph: 11 + x > -5
-11
-11
x > -16
Check: 11 + (-16) = -5 True
Check 2: 11 + (-15) > -5 True
-16
0
SOLVING INEQUALITIES
Using Addition and Subtraction
SAMPLE PROBLEMS
Solve: 55 – x > 70
-55
NOTE: sign stays with x 
-55
-x > 15
Change signs
x > -15
Check: 55 – (-15) = 70 True
Check 2: 55 – (-14) > 70 False…WHY?
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
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!!
SOLVING INEQUALITIES
Using Multiplication and Division
Just like solving equations, except…
…when multiplying or dividing by a negative.
SOLVE: -3x > 6
-3
-3
x < -2
Ding!!
SOLVING INEQUALITIES
Using Multiplication and Division
Just like solving equations, except…
…when multiplying or dividing by a negative.
x
 6 (-2)
SOLVE: (-2)
2
x < 12
Ding!!
SOLVING INEQUALITIES
Using Multiplication and Division
Just like solving equations, except…
…when multiplying or dividing by a negative.
SOLVE: 3x – 12 > 5x + 4
-5x
-5x
-2x – 12 > 4
+12
+12
-2x > 16
-2
-2
x<
> -8
Ding!!