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HOMEWORK HELP
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INT
Extra help with
problem solving in
Exs. 32–40 is available at
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SOLVING ABSOLUTE-VALUE EQUATIONS Solve the equation and check
your solutions. If the equation has no solution, write no solution.
32. ⏐6x 4⏐ 2
33. ⏐4x 2⏐ 22
34. ⏐3x 5⏐ 22
35. ⏐2x 5⏐ 3
36. ⏐6x 3⏐ 39
37. ⏐2x 7⏐ 9
38. ⏐5 4x⏐ 3 4
39. ⏐2x 4⏐ 8 10
40. ⏐5x 4⏐ 3 19
ABSOLUTE-VALUE EQUATIONS Match the absolute-value equation with
its graph.
41. ⏐x 2⏐ 6
42. ⏐x 6⏐ 2
A.
6 units
12 10
8
B.
6
4
6 units
2
0
6 units
8
6
4
2
2
4
2 units
0
1
2
3
2
4
6
8
8
10
12
8
9
10
6 units
0
C.
43. ⏐x 2⏐ 6
4
6
2 units
5
6
7
WRITING ABSOLUTE-VALUE EQUATIONS Write an absolute-value
Careers
equation that has the given solutions.
44. 8 and 18
45. 6 and 10
46. 2 and 9
ASTRONOMY In Exercises 47 and 48,
use the following information.
The distance between Earth and the
sun is not constant, because Earth’s
orbit around the sun is an ellipse.
The maximum distance from Earth
to the sun is 94.5 million miles.
The minimum distance is about
91.4 million miles.
Sun
Not drawn to scale
Earth
47. Graph the maximum and minimum distances on a number line and locate the
ASTRONOMERS study
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energy, matter, and natural
processes throughout the
universe. Professional
astronomers need a doctoral
degree. Nevertheless,
amateur astronomers make
important discoveries as well.
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midpoint. Determine the distance from the midpoint to the minimum and
from the midpoint to the maximum.
48. Use your answers from Exercises 47 to write an absolute-value equation
that has the minimum and maximum distances between Earth and the sun
(in millions of miles) as its solutions.
49. CHALLENGE The highest elevation in North America is 20,320 feet above
sea level at Mount McKinley. The lowest elevation is 282 feet below sea
level in Death Valley. Find an absolute-value equation that has the highest
and lowest elevations in North America as its solutions.
6.6
Solving Absolute-Value Equations
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