The procedure to solve a polynomial or rational inequality may be applied to all inequalities of the f ( x ) > 0 , f ( x ) < 0 , f ( x ) ≥ 0 and f ( x ) ≤ 0 . That is, find the real solutions to the related equation and determine restricted values of x . Then determine the sign of f ( x ) on each interval defined by the boundary points. Use this process to solve the inequalities in Exercises 109–120 1 x − 2 − 4 ≤ 0
The procedure to solve a polynomial or rational inequality may be applied to all inequalities of the f ( x ) > 0 , f ( x ) < 0 , f ( x ) ≥ 0 and f ( x ) ≤ 0 . That is, find the real solutions to the related equation and determine restricted values of x . Then determine the sign of f ( x ) on each interval defined by the boundary points. Use this process to solve the inequalities in Exercises 109–120 1 x − 2 − 4 ≤ 0
Solution Summary: The author calculates the solution of the inequality 1sqrtx-2-4le 0 by dividing the x-axis into intervals defined by the boundary points.
The procedure to solve a polynomial or rational inequality may be applied to all inequalities of the
f
(
x
)
>
0
,
f
(
x
)
<
0
,
f
(
x
)
≥
0
and
f
(
x
)
≤
0
. That is, find the real solutions to the related equation and determine restricted values of x. Then determine the sign of
f
(
x
)
on each interval defined by the boundary points. Use this process to solve the inequalities in Exercises 109–120
1) Express these large and small numbers from the Read and Study section in scientific
notation:
(a) 239,000 miles
(b) 3,800,000,000,000 sheets of paper
(c) 0.0000000000000000000000167 grams
2) Find all values for the variable x that make these equations true.
(a) 5x = 1
(b) 3x = 1/1
9
(c) 4* = 11/
4
(e) 4* = 64
(g) 10x = 1,000,000
(d) 3x=-3
(f) 2x =
=
8
(h) 10x = 0.001
(b)
4) Find an equation to fit each of the following graphs:
(a)
20
20
18
16
14
12
10
8
6
4
2
24
22
20
18
16
14
12
10
8
16
A
2
-3 -2
-1-0
2
3
4.
-1
0
1
2
3.
-2
-2
3) Which of the following are equivalent to 3? (There may be more than one that is
equivalent!)
-1
(a) (9)¯¹
3.
(b) (-3)-1
(c) (-3)
-1
(d) -(¯3)
(e) 11
3-1
(f) 3-4
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