Solving Inequalities

Exploring InequalitiesPhrase Symbol Examples

is less than

Exploring InequalitiesPhrase Symbol Examples

is less than <

Exploring InequalitiesPhrase Symbol Examples

is less than < 1 < 2, 100 < 1000

Exploring InequalitiesPhrase Symbol Examples

is less than < 1 < 2, 100 < 1000

is less than or equal to

Exploring InequalitiesPhrase Symbol Examples

is less than < 1 < 2, 100 < 1000

is less than or equal to ≤

Exploring InequalitiesPhrase Symbol Examples

is less than < 1 < 2, 100 < 1000

is less than or equal to ≤ 1 ≤ 2, 2 ≤ 2, 100 ≤ 1000

Exploring InequalitiesPhrase Symbol Examples

is less than < 1 < 2, 100 < 1000

is less than or equal to ≤ 1 ≤ 2, 2 ≤ 2, 100 ≤ 1000

is greater than

Exploring InequalitiesPhrase Symbol Examples

is less than < 1 < 2, 100 < 1000

is less than or equal to ≤ 1 ≤ 2, 2 ≤ 2, 100 ≤ 1000

is greater than >

Exploring InequalitiesPhrase Symbol Examples

is less than < 1 < 2, 100 < 1000

is less than or equal to ≤ 1 ≤ 2, 2 ≤ 2, 100 ≤ 1000

is greater than > 1 > 0, 100 > 10

Exploring InequalitiesPhrase Symbol Examples

is less than < 1 < 2, 100 < 1000

is less than or equal to ≤ 1 ≤ 2, 2 ≤ 2, 100 ≤ 1000

is greater than > 1 > 0, 100 > 10

is greater than or equal to

Exploring InequalitiesPhrase Symbol Examples

is less than < 1 < 2, 100 < 1000

is less than or equal to ≤ 1 ≤ 2, 2 ≤ 2, 100 ≤ 1000

is greater than > 1 > 0, 100 > 10

is greater than or equal to

≥

Exploring InequalitiesPhrase Symbol Examples

is less than < 1 < 2, 100 < 1000

is less than or equal to ≤ 1 ≤ 2, 2 ≤ 2, 100 ≤ 1000

is greater than > 1 > 0, 100 > 10

is greater than or equal to

≥ 1 ≥ 0, 1 ≥ 1, 100 ≥ 10

Graph the solution of an inequality on a number line for t > 4:

0 1 2 3 4 5 6 7 8 9 10

Graph the solution of an inequality on a number line for t > 4:

Use an open circle if the inequality is > or < :

0 1 2 3 4 5 6 7 8 9 10

Graph the solution of an inequality on a number line for t > 4:

Shade the direction which includes all possible answers.

0 1 2 3 4 5 6 7 8 9 10

Graph the solution of an inequality on a number line for y ≤ 8:

0 1 2 3 4 5 6 7 8 9 10

Graph the solution of an inequality on a number line for y ≤ 8:

Use a closed circle if the inequality is ≥ or ≤:

0 1 2 3 4 5 6 7 8 9 10

Graph the solution of an inequality on a number line for y ≤ 8:

Shade the direction which includes all possible answers.

0 1 2 3 4 5 6 7 8 9 10

Complete the TableInequalit

yWhole

number solutions of

the inequality

Equation Solution of

equation

Solution of inequality

x + 1 < 6 x + 1 = 6

Complete the TableInequalit

yWhole

number solutions of

the inequality

Equation Solution of

equation

Solution of inequality

x + 1 < 6 0, 1, 2, 3, 4 x + 1 = 6

Complete the TableInequalit

yWhole

number solutions of

the inequality

Equation Solution of

equation

Solution of inequality

x + 1 < 6 0, 1, 2, 3, 4 x + 1 = 6 x = 5

Complete the TableInequalit

yWhole

number solutions of

the inequality

Equation Solution of

equation

Solution of inequality

x + 1 < 6 0, 1, 2, 3, 4 x + 1 = 6 x = 5 x < 5

Complete the TableInequalit

yWhole

number solutions of

the inequality

Equation Solution of

equation

Solution of inequality

x + 1 < 6 0, 1, 2, 3, 4 x + 1 = 6 x = 5 x < 5

x – 3 > 0 x – 3 = 0

Complete the TableInequalit

yWhole

number solutions of

the inequality

Equation Solution of

equation

Solution of inequality

x + 1 < 6 0, 1, 2, 3, 4 x + 1 = 6 x = 5 x < 5

x – 3 > 0 4, 5, 6, 7, 8, 9 x – 3 = 0

Complete the TableInequalit

yWhole

number solutions of

the inequality

Equation Solution of

equation

Solution of inequality

x + 1 < 6 0, 1, 2, 3, 4 x + 1 = 6 x = 5 x < 5

x – 3 > 0 4, 5, 6, 7, 8, 9 x – 3 = 0 x = 3

Complete the TableInequalit

yWhole

number solutions of

the inequality

Equation Solution of

equation

Solution of inequality

x + 1 < 6 0, 1, 2, 3, 4 x + 1 = 6 x = 5 x < 5

x – 3 > 0 4, 5, 6, 7, 8, 9 x – 3 = 0 x = 3 x > 3

Complete the TableInequalit

yWhole

number solutions of

the inequality

Equation Solution of

equation

Solution of inequality

x + 1 < 6 0, 1, 2, 3, 4 x + 1 = 6 x = 5 x < 5

x – 3 > 0 4, 5, 6, 7, 8, 9 x – 3 = 0 x = 3 x > 3

x + 1 ≤ 5 x + 1 = 5

Complete the TableInequalit

yWhole

number solutions of

the inequality

Equation Solution of

equation

Solution of inequality

x + 1 < 6 0, 1, 2, 3, 4 x + 1 = 6 x = 5 x < 5

x – 3 > 0 4, 5, 6, 7, 8, 9 x – 3 = 0 x = 3 x > 3

x + 1 ≤ 5 0, 1, 2, 3, 4 x + 1 = 5

Complete the TableInequalit

yWhole

number solutions of

the inequality

Equation Solution of

equation

Solution of inequality

x + 1 < 6 0, 1, 2, 3, 4 x + 1 = 6 x = 5 x < 5

x – 3 > 0 4, 5, 6, 7, 8, 9 x – 3 = 0 x = 3 x > 3

x + 1 ≤ 5 0, 1, 2, 3, 4 x + 1 = 5 x = 4

Complete the TableInequalit

yWhole

number solutions of

the inequality

Equation Solution of

equation

Solution of inequality

x + 1 < 6 0, 1, 2, 3, 4 x + 1 = 6 x = 5 x < 5

x – 3 > 0 4, 5, 6, 7, 8, 9 x – 3 = 0 x = 3 x > 3

x + 1 ≤ 5 0, 1, 2, 3, 4 x + 1 = 5 x = 4 x ≤ 4

Complete the TableInequalit

yWhole

number solutions of

the inequality

Equation Solution of

equation

Solution of inequality

x + 1 < 6 0, 1, 2, 3, 4 x + 1 = 6 x = 5 x < 5

x – 3 > 0 4, 5, 6, 7, 8, 9 x – 3 = 0 x = 3 x > 3

x + 1 ≤ 5 0, 1, 2, 3, 4 x + 1 = 5 x = 4 x ≤ 4

2x ≥ 4 2x = 4

Complete the TableInequalit

yWhole

number solutions of

the inequality

Equation Solution of

equation

Solution of inequality

x + 1 < 6 0, 1, 2, 3, 4 x + 1 = 6 x = 5 x < 5

x – 3 > 0 4, 5, 6, 7, 8, 9 x – 3 = 0 x = 3 x > 3

x + 1 ≤ 5 0, 1, 2, 3, 4 x + 1 = 5 x = 4 x ≤ 4

2x ≥ 4 2, 3, 4, 5, 6, 7, 8, 9

2x = 4

Complete the TableInequalit

yWhole

number solutions of

the inequality

Equation Solution of

equation

Solution of inequality

x + 1 < 6 0, 1, 2, 3, 4 x + 1 = 6 x = 5 x < 5

x – 3 > 0 4, 5, 6, 7, 8, 9 x – 3 = 0 x = 3 x > 3

x + 1 ≤ 5 0, 1, 2, 3, 4 x + 1 = 5 x = 4 x ≤ 4

2x ≥ 4 2, 3, 4, 5, 6, 7, 8, 9

2x = 4 x = 2

Complete the TableInequalit

yWhole

number solutions of

the inequality

Equation Solution of

equation

Solution of inequality

x + 1 < 6 0, 1, 2, 3, 4 x + 1 = 6 x = 5 x < 5

x – 3 > 0 4, 5, 6, 7, 8, 9 x – 3 = 0 x = 3 x > 3

x + 1 ≤ 5 0, 1, 2, 3, 4 x + 1 = 5 x = 4 x ≤ 4

2x ≥ 4 2, 3, 4, 5, 6, 7, 8, 9

2x = 4 x = 2 x ≥ 2

Solve and Graph each inequality

•3x > 6

• ≤ 12

•x – 5 < 8

•x + 7 ≥ 10

2

x

Solve and Graph each inequality

•3x > 6 x > 2 0 1 2 3 4 5 6 7 8 9

• ≤ 12

•x – 5 < 8

•x + 7 ≥ 10

2

x

Solve and Graph each inequality

•3x > 6

• ≤ 12

x ≤ 24 18 19 20 21 22 23 24 25

•x – 5 < 8

•x + 7 ≥ 10

2

x

Solve and Graph each inequality

•3x > 6

• ≤ 12

•x – 5 < 8 x < 13 9 10 11 12 13 14

15 16

•x + 7 ≥ 10

2

x

Solve and Graph each inequality

•3x > 6

• ≤ 12

•x – 5 < 8

•x + 7 ≥ 10 x ≥ 3 0 1 2 3 4 5 6 7

8

2

x

Example: Six friends go to a restaurant. They have a gift certificate for $150. They plan to share it equally and spend no additional money. Write an inequality to describe how much each friend can spend.

Example: Six friends go to a restaurant. They have a gift certificate for $150. They plan to share it equally and spend no additional money. Write an inequality to describe how much each friend can spend.

Write an inequality to represent the situation:

Example: Six friends go to a restaurant. They have a gift certificate for $150. They plan to share it equally and spend no additional money. Write an inequality to describe how much each friend can spend.

Write an inequality to represent the situation:

6x ≤ 150

Example: Six friends go to a restaurant. They have a gift certificate for $150. They plan to share it equally and spend no additional money. Write an inequality to describe how much each friend can spend.

Write an inequality to represent the situation:

6x ≤ 150

What operation should you use to isolate the

variable?

Example: Six friends go to a restaurant. They have a gift certificate for $150. They plan to share it equally and spend no additional money. Write an inequality to describe how much each friend can spend.

Write an inequality to represent the situation:

6x ≤ 150

What operation should you use to isolate the

variable? Division

Example: Six friends go to a restaurant. They have a gift certificate for $150. They plan to share it equally and spend no additional money. Write an inequality to describe how much each friend can spend.

Write an inequality to represent the situation:

6x ≤ 150

≤ 6

6x6

150

Example: Six friends go to a restaurant. They have a gift certificate for $150. They plan to share it equally and spend no additional money. Write an inequality to describe how much each friend can spend.

Write an inequality to represent the situation:

6x ≤ 150

≤ x ≤ $25

6

6x6

150

Graphing Inequalities

Inequality Graph

x < 5

x ≤ 5

x > 5

x ≥ 5