Download Inequalities - Souderton Math

Inequalities
Objective: To solve and graph all
types of inequalities.
Inequalities and Their Graphs
• What inequality represents the verbal expression?
• All real numbers x less than or equal to -7.
• 6 less than a number k is greater than 13.
Inequalities and Their Graphs
• What inequality represents the verbal expression?
• All real numbers x less than or equal to -7.
_______|_____|_____

x  7
7
0
• 6 less than a number k is greater than 13.
Inequalities and Their Graphs
• What inequality represents the verbal expression?
• All real numbers x less than or equal to -7.
_______|_____|_____

x  7
7
0
• 6 less than a number k is greater than 13.
____|_______|_________
k  6  13
0
19
k  6  6  13  6
k  19
Inequalities and Their Graphs
• Are the following a solution of 2x  1  3 ?
-3
-1
Inequalities and Their Graphs
• Are the following a solution of 2x  1  3 ?
-3
2(3)  1  3
 6  1  3
 5  3
false
Not a solution
-1
Inequalities and Their Graphs
• Are the following a solution of 2x  1  3 ?
-3
2(3)  1  3
 6  1  3
 5  3
false
Not a solution
-1
2(1)  1  3
 2  1  3
 1  3 true
Is a solution
Inequalities and Their Graphs
• Are the following a solution of 2x  1  3 ?
-3
no
2 x  1  3
2 x  4
x  2
-1
yes
Graphs
• What inequality represents the graph?
______|__________|_______

0
3

______|__________|________
1
0
Graphs
• What inequality represents the graph?
______|__________|_______

0
3

______|__________|________
1
x3
0
x  1
Homework
• Page 168
• 9-37 odd
Addition/Subtraction
• What are the solutions of
x 15  12
? Graph.
Addition/Subtraction
• What are the solutions of
x 15  12
? Graph.
• Add 15 to both sides. x  15  15  12  15
x3
____|________|_____________

0
3
Addition/Subtraction
• What are the solutions of
t  6  4
? Graph.
Addition/Subtraction
• What are the solutions of
t  6  4
• Subtract 6 from both sides.
? Graph.
t  6  6  4  6
t  10
____________|_______|______

 10
0
Class Work
• Page 174
• 14-28 even
Homework
• Pages 174-175
• 13-27 odd
• 33-41 odd
Multiplication/Division
• What are the solutions of
x
 2
3
? Graph.
Multiplication/Division
• What are the solutions of
• Multiply each side by 3

x
 2
3
? Graph.
x
3   2  3
3
x  6
________|__________|________
6
0
Multiplication/Division
• Everything in the last problem was the same as an
equation. With an inequality, the only difference is
that when you multiply or divide by a negative
number you switch the inequality sign.
Multiplication/Division
• Everything in the last problem was the same as an
equation. With an inequality, the only difference is
that when you multiply or divide by a negative
number you switch the inequality sign.
52
Multiplication/Division
• Everything in the last problem was the same as an
equation. With an inequality, the only difference is
that when you multiply or divide by a negative
number you switch the inequality sign.
52
5(3)  2(3)
 15  6 ?
no
Multiplication/Division
• Everything in the last problem was the same as an
equation. With an inequality, the only difference is
that when you multiply or divide by a negative
number you switch the inequality sign.
52
5(3)  2(3)
 15  6 ?
yes
Multiplication/Division
• What are the solutions of
 9 y  63
? Graph.
Multiplication/Division
• What are the solutions of
 9 y  63
• Divide each side by -9.
• Switch the inequality sign!!
7
? Graph.
 9 y  63

9
9
y7
_______|_______|________
0
Class Work
• Page 181
• 8-18 even
Homework
• Page 181
• 7 -29 odd
Class Work
• Page 190
• 18-34 even
Homework
• Page 190
• 17-39 odd