9-6 Inequalities
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Transcript 9-6 Inequalities
9.6 Solving Inequalities Using
Addition and Subtraction
Day 1 Graphing
What symbol is this?
17.2
>
0.985
Many students can’t tell them apart.
reater than
>
<
ess than
Inequality Symbols
1)
2)
3)
4)
5)
“is greater than or equal to”
“is less than”
“is equal to”
“is less than or equal to”
“is greater than”
How can you graphically show the following?
1) x 2
-5 -4 -3 -2 -1 0
1
2
3 4
5
1
2
3 4
5
2) x 3
-5 -4 -3 -2 -1 0
How to graph inequalities
• Place a circle on the #
• If it is < or > leave the circle un-shaded,
if it is ≤ or ≥ shade the circle
• When x is on the left hand side,
if it is > or ≥ shade to the right
if it is < or ≤ shade to the left
Graph the solution of
x < -1
-1
0
Graph the solution of
x > -2
-6
-4
-2
0
2
4
6
Graph the solution of
x -2
If you have ≤ or ≥ you draw a closed circle
-6
-4
-2
0
2
4
6
Write the inequality shown in this graph
-6
-4
-2
0
2
x4
4
6
Write the inequality shown in this graph
-6
-4
-2
0
2
x 2
4
6
Write an inequality that describes each graph below.
1) x 2
-4 -3 -2 -1 0 1 2 3 4
2) x 1
4) x 9
-9
5) x 15
-4 -3 -2 -1 0 1 2 3 4
3) x 0
-4 -3 -2 -1 0 1 2 3 4
0
0
15
6) x 24
-24
0
Write an inequality that represents each statement
and graph.
1) All real numbers less than or equal to 3.
x3
-5 -4 -3 -2 -1 0 1
2
3
4
5
2) All real numbers greater than -2.
x 2
-5 -4 -3 -2 -1 0 1 2 3
4
5
3) All real numbers less than -4.
x 4
-5 -4 -3 -2 -1 0 1 2
4
5
3
Write two inequalities for the
phrase
• All real numbers less than 2
x2
2 x
• All real numbers greater than or equal to 0
x0
0 x
Homework
• Page 478 (1-7, 12-28) all
9.6
Solving Inequalities Using
Addition and Subtraction
Day 2
Solving Inequalities
Solve
Mentally
Equations
Inequalities
x+3=5
x+3>5
x=2
x+3=5
Solve Using
- 3 -3
Transformations
x=2
x is any real
number
greater than 2.
x+3>5
- 3 -3
x>2
Solve the inequalities below and graph.
1) x 5 7
3) 6 x 2
2
2
5 5
4 x
x 2
x 4
-4 -3 -2 -1 0 1 2 3 4
2)
x45
4 4
x 1
-4 -3 -2 -1 0 1 2 3 4
-4 -3 -2 -1 0 1 2 3 4
4) 5 y 8
8
8
3 y
y 3
-4 -3 -2 -1 0 1 2 3 4
Solve the inequalities below and graph.
1) 16 x 4
3) m 19 40
19 19
4
4
20 x
x 20
m 59
0
20
2) y 7 11
7 7
y 18
-18
0
0
59
4) 36 x 12
12
12
24 x
x 24
0
24
Homework
• Page 479 (29-43) all