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
x4
2
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.
x3
-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
x2
2x
• All real numbers greater than or equal to 0
x0
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)
x45
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
m  59
x  20
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