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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
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