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

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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.

5x >

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.

12x >

Verbal expressions that suggest an inequality.

WRITING INEQUALITIES

Two less than a number is less than three.

– 2

Verbal expressions that suggest an inequality.

WRITING INEQUALITIES

Two less than a number is less than three.

– 2

Verbal expressions that suggest an inequality.

x

WRITING INEQUALITIES

Two less than a number is less than three.

– 2

Verbal expressions that suggest an inequality.

x <

WRITING INEQUALITIES

Two less than a number is less than three.

– 2

Verbal expressions that suggest an inequality.

x < 3

WRITING INEQUALITIES

TRY THESE

Verbal expressions that suggest an inequality.

The sum of eight and a number is at least six.

8 + x > 6

WRITING INEQUALITIES

TRY THESE

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

SOLVING INEQUALITIESUsing Addition and Subtraction

SAMPLE PROBLEMS

Solve & Graph: x – 3 > 7+3 +3

x > 10Check: 10 – 3 = 7 True

Check 2: 11 – 3 > 7 True

0 10

SAMPLE PROBLEMS

Solve & Graph: x + 6 < 2-6 -6

x < - 4Check: - 4 + 6 = 2 True

SOLVING INEQUALITIESUsing Addition and Subtraction

Check 2: - 5 + 6 < 2 True

- 4 0

SAMPLE PROBLEMS

Solve & Graph: 11 + x > - 5-11 -11

x > - 16Check: 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

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

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 > -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