"For HELPCLICK only!!"_BIO II and College Math_forum-B
AlphaMann
collegemath_1_7-for-helpclick.pptSection 1.7
Solving Inequalities
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Write each inequality using interval notation:
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Write each interval as an inequality involving x.
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Express as an inequality the result of multiplying each side of the inequality 3 < 5 by 2.
3(2) < 5(2)
6 < 10
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Note to keep this inequality true, the inequality symbol must be reversed.
Express as an inequality the result of multiplying each side of the inequality 3 < 5 by –2.
3(–2) ? 5(–2)
–6 > –10
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]
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)
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)
(
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]
[
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(
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In electricity, Ohm’s law states that E = IR, where E is the voltage (in volts). I is the current (in amperes), and R is the resistance (in ohms). An air-conditioning unit is rated at a resistance of 10 ohms. If the voltage varies from 110 to 120 volts, inclusive, what corresponding range of current will the air conditioner draw?
The air conditioner will draw between 11 and 12 amperes of current, inclusive.
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)24
ax
-££
)27
bx
<<
)6
cx
³
)3
dx
<-
[
]
2,4
-
(
)
2,7
-
[6,)
¥
(,3]
-¥-
12
x
-<£
20
x
-££
5
x
>
1
x
<
)(1,2]
a
-
)(5,)
c
¥
)[2,0]
b
-
)(,1)
d
-¥
Solve the inequality: 531 and graph the
solution set.
x
-³-
5
531
5
x
-³-
--
36
x
-³-
36
33
x
£
--
--
2
x
£
{
}
2 or (,2]
xx
-¥
£
Solve the inequality: 4321 and graph th
e solution set.
xx
+<-
42
3
31
3
xx
<
-
--
+
{
}
2 or (,2)
xx
<--¥-
424
xx
<-
424
22
xx
xx
-
<-
-
24
x
<-
24
22
x
-
<
2
x
<-
Solve the inequality: 1325 and graph th
e solution set.
x
-<+<
132 and 325
xx
-<++<
{
}
11 or (1,1)
xx
-<<-
132
22
x
-
-+
-
<
33
x
-<
33
33
x
-
<
1
x
-<
2
3
2
25
x
+
-
<
-
33
x
<
33
33
x
<
and 1
x
<
52
13
3
Solve the inequality: and graph the so
lution set.
x
-
££
(
)
(
)
5
13
333
2
3
x
-
æö
££
ç÷
èø
{
}
21 or [2,1]
xx
-££-
3529
x
£-£
35
5
2
5
9
5
x
£-£
---
224
x
-£-£
22
22
4
2
x
-
-
-
³³
--
12
x
³³-
21
x
-££
(
)
1
Solve the inequality: 36>0 and graph th
e solution set.
x
-
+
(
)
1
1
36=0
36
x
x
-
+>
+
{
}
2 or (2,)
xx
>--¥
By the reciprocal property: 360
x
+>
36
x
>-
2
x
>-
If 32, find and so that 32.
xabaxb
-<<<+<
(
)
(
)
33332
x
-<<
32
x
-<<
936
x
-<<
923262
x
-+<+<+
7328
x
-<+<
So 7 and 8
ab
=-=
110120
E
££
110120
IR
££
110(10)120
I
££
110(10)120
101010
I
££
1112
I
££
