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Step 3
It appears that 2
≤
x
≤
7. You can test some
x
-values to confirm the solution.
Use three test values: one less than 2, one between 2 and 7, and one greater
than 7. Organize the test values in a table.
x
=
0
x
=
4
x
=
9
3
+
√
5(0)
-
10
8
3
+
√
-
10
≤
8
✗
Because
√
-
10is not a
real number, the
inequality is not satisfied.
3
+
√
5(4)
-
10
8
6.16
≤
8
✓
Because 6.16
≤
8, the
inequality is satisfied.
3
+
√
5(9)
-
10
8
8.92
≤
8
✗
Because 8.92
≰
8, the
inequality is not satisfied.
The solution checks. Only values in the interval 2
≤
x
≤
7 satisfy the inequality. You
can summarize the solution with a number line.
C07-036A-888482
10
10 8 6
2 4 6 8
2 4
0
Guided Practice
Solve each inequality.
4A.
√
2
x
+
2
+
1
≥
5
4B.
√
4
x
-
4
-
2
<
4
Check your mastery of
solving radical inequalities
by using the
Self-Check
Quiz
in ConnectED.
Check Your Understanding
=
Step-by-Step Solutions begin on page R14.
Solve each equation.
1.
√
x
-
4
+
6
=
10
2.
√
x
+
13
-
8
= -
2
3.
8
-
√
x
+
12
=
3
4.
√
x
-
8
+
5
=
7
3
√
x
-
2
=
3
6.
(
x
-
5)
1
_
3
-
4
= -
2
7.
(4
y
)
1
_
3
+
3
=
5
8.
3
√
n
+
8
-
6
= -
3
9.
√
y
-
7
=
0
10.
2
+
4
z
1
_
2
=
0
11.
5
+
√
4
y
-
5
=
12
12.
√
2
t
-
7
=
√
t
+
2
13.
REASONING
The time
T
in seconds that it takes a pendulum to make a complete
swing back and forth is given by the formula
T
=
2
π
√
L
_
g
, where
L
is the length of the
pendulum in feet and
g
is the acceleration due to gravity, 32 feet per second squared.
a.
In Tokyo, Japan, a huge pendulum in the Shinjuku building measures 73 feet 9.75
inches. How long does it take for the pendulum to make a complete swing?
b.
A clockmaker wants to build a pendulum that takes 20 seconds to swing back and
forth. How long should the pendulum be?
14.
MULTIPLE CHOICE
Solve (2
y
+
6)
1
_
4
-
2
=
0.
A
y
=
1
B
y
=
5
C
y
=
11
D
y
=
15
Solve each inequality.
15.
√
3
x
+
4
-
5
≤
4
16.
√
b
-
7
+
6
≤
12
17.
2
+
√
4
y
-
4
≤
6
18.
√
3
a
+
3
-
1
≤
2
19.
1
+
√
7
x
-
3
>
3
20.
√
3
x
+
6
+
2
≤
5
21.
-
2
+
√
9
-
5
x
≥
6
22.
6
-
√
2
y
+
1
<
3
Examples 1–2
5
Example 3
Example 4
for a
Self-Check Quiz
connectED.mcgraw-hill.com355