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Name ________________________________________ Date __________________ Class__________________
LESSON
5-8
Practice A
Solving Radical Equations and Inequalities
Rewrite each equation to isolate the radical.
1.
x 60
2. 8  3 x  x  0
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2 x  1  17  3 x
3.
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Identify to what power each equation must be raised in order to solve.
Then solve.
4.
x 4
5.
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4
3 x  12
6.
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3
x 1 4
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Solve the equation. Then identify any extraneous solutions.
7. 2 x  2  4
8.
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x 3 x 3
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Solve each equation or inequality.
9.
x 2 5
10.
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11.
1
 x  1 3
6
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12. 2 x  3  10
3
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13.
1
 4x 2
2x  6  0
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14.
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3x  1  8
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Solve.
15. Ainsley and Ben each solve the inequality
x  3  5  10 . Ainsley’s solution
is x  22. Ben’s solution is 3  x  22. Why are their solutions different?
Which is correct?
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Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
5-59
Holt McDougal Algebra 2
4. a. −1
Challenge
1. y = 3 − x + 1 − 4
b. 1
c. −3
2. y = 4 3 x + 2 − 3
d. 2
3. y = −0.5 − x + 5 + 2
e. Translated 2 units up, 3 units left,
and reflected across the x-axis
4. y = 5 3 − x − 1 + 4
5-8 SOLVING RADICAL EQUATIONS
Problem Solving
AND INEQUALITIES
5
1. a. d (a ) = 3.56
a
9
Practice A
b.
1.
x =6
2.
3.
2 x + 1 = 3x + 17
4. 2; x = 16
5. 4; x =
69
2
3x = x − 8
6. 3; x = 63
7. x = 2; no extraneous solutions
8. x = 1, x = 6; x = 1 is an extraneous
solution.
c. 36 km; 27 km
2. B
3. C
4. D
5. A
9. x = 23
10. x = 9
11. x = 26
12. x = 28
13. 0 ≤ x ≤ 18
14. x ≥ 21
15. Ben’s solution is correct. Ainsley forgot
that the radicand cannot be negative.
6. D
Reading Strategies
Practice B
1. a. 1
b. 1
c. 0
d. −3
e. Translated 3 units down
2. a. −1
1. x = 43
2. x = 20
3. x = 6
4. x =
1
2
5. x = −15
6. x =
1
4
b. 1
7. No solutions, since both −1 and −7 are
extraneous
c. 1
8. x = 32
d. 2
10. x = −52
11. −2 ≤ x ≤ 1
e. Translated 2 units up, 1 unit right,
and reflected across the x-axis
12. x > 40
13.
14. x > 44
15. 25 years
3. a. 1
b. −1
9. x = 7
1
≤ x ≤8
2
Practice C
c. −4
d. −5
e. Translated 5 units down, 4 units left,
and reflected across the y-axis
1. x = 31
2. x = 47
3. x = 7
4. x = 9
5. x = −2 and x = 1
6. x = 5
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
A66
Holt McDougal Algebra 2