Inequalities Notes
An inequality is an open sentence that contains the
symbols <, >,
^. For example: 3x > 7
o
Graph the solutions to the following inequalities on a
number line.
1. x > 5
2. x<5
-O
0
S
4. x > - 4
.
0
Solve the following inequalities, then graph the solutions
on a number line.
6. 7 < 2 x - 3
5. 3 x - 9 > l
3X
X>
o
I I I M
:
7. -5x - 8 >7
1 1 1 1 1 4
8. V -5<4
2
X-IO<
-r
-v
-HO
X< -3
-3
-*—\—v-v
o
\ \ i \ \ \ l, I l 1 i U 1 I. M 1
"
-^ x
9. '
-9
5>3
<7
X
< I )
\
-3
M \ 1 )
-75~
-70
£-
-<5to
11. 6-6(4a + 7 ) > 3 6
36,
>3
>
-3
12. -3 (8 + 2n) < -3 (8 - 6n) + 8n
^
H-4-+^
Solve, then graph each compound inequality
Qx
13.
4
<-l or x - 4 > -6
o
M ) I I I 1V
14. -6 < -1 + n < -5
-H
t/
4-1
.-•
i
\
\
15. - 3 v > 1 2 o r v - 3 >
^
~=3
f3 t.
V>3
-y
16. 6 + x<9and-Jx<_35_
"^
~^
-7
,
3
17. -32<4a + 4 < 3 6
<
-
A <
<a<
&
0
18. l-3x>10or-10 + 7x>-3
7x:>
_
-7 - -7
.<- -0
S ^
-3
_
-3
0
i
)
)
—
^
19. -1<2 - ^ 3 a < 5
-£
^ ^ ^< 3
^^n
-3
/ ^x
^A
3
—^^- •<-.
3 - f-<T
^
^'
20. 4 + k < 4 a n d 2 k - 3 > - 5
43 ' " "
(<
/
'
)
1
'
\
Unit 2
Inequalities Notes Supplement
Write an inequality for the graph.
1.
I
I
I
I
I
I
I
j
1
1
- 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1 0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
h
9
^ -3
2.
<
I
I
I
I
I
I
I
I
I
- 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1 0
1
1
1
1
1
1
2
3
4
5
6
7
8
1—Q
I
I
I )
9
3.
< -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 — Q
- 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1 0
1
2
3
4
5
6
7
8
I I I I
9
4.
i
i
i
- 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1 0
i
i
i
i
i
i
1
2
*—i—i—i—i—i—h
3
4
5
6
7
8
9
Write a compound inequality for the graph.
5.
I
I
I
* -1 - Q
- 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1 0
I
I
I
I
I
I
I
I
I
1
2
3
r <3
>:...
4
5
I
6
I
7
I
8
I
9
/'•
6.
(
I
I
I
I
I
I
I
I
Q -1 -1 - Q
- 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1 0
1
2
3
I
I
I
I
I
I
4
5
6
7
8
9
I )
/
7.
<-1-1-1-1-1-f
I I I I I Q-1-1-1-1-1-1-1—
- 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1 0
1 2
3
4
5
6
7
8
9
-Lf < n < £
8.
< - 1 -1 -1 -1 - 1 -1 -1 -1 — Q
- 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1 0
-
I <
1
)
I I I I I * -1 -1 -1 2
3
4
5
6
7
8
9
"
9.
< -1 -1 — Q
I I I I Q - 1 -1 -1 -1 -1 -1 - 1 -1 -1 -1 -
- 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1 0
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
-7 < n <
10.
- 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1 0
-3 ^ n £ 5"