Download 2x2\ 3 }

LESSON
5.6
Answers for the lesson “Solve Rational
Equations”
Skill Practice
26. The student “cross multiplied”
1. cross multiplying
2. 4; 4 is not in the domain of the
equation because you cannot
divide by zero.
3. Graph both sides of the equation.
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
If the graphs intersect at a
possible solution, then it is a
solution. If the graphs do not
intersect at a possible solution,
then it is an extraneous solution.
the fractions on the left side of
the equation. Both sides of the
equation should have been
multiplied by the LCD, 2x 2;
1 2x
2
4
3
2x 2 }
1 }2 5 2x 2(1),
x
3x 1 8 5 2x 2.
27. The student simply added
4. 4
5. 6
6. 5
numerators and denominators on
the left side of the equation. Both
sides of the equation should have
been multiplied by the LCD, 6x;
7. 2
8. 3
9. 21
6x1 }x 1 }
5 6x 1 }
,
62
x2
10. 61
11. no solution
12. 6
13. A
23
45
30 1 23x 5 270.
14. 1, 4
}
23 6 Ï 129
4
15. 4
16. }
7
17. 2}
3
18. 1, 6
}
21 6 Ï 79
19. }
3
20. 22, 3
21. 1
3
22. 2}, 2
2
5
23. 2}, 8
2
24. no solution
25. 0, 7
5
28. C
2x
6
29. Sample answer: } 5 };
x21
x15
5
12
4
}1}5}
3
x
x
30. Always true; when x 5 a, the
denominators of the fractions
are zero.
31. Sometimes true; the equation will
have exactly one solution except
when a 5 3.
32. Always true; the only apparent
solution is an extraneous solution.
Algebra 2
Answer Transparencies for Checking Homework
177
Problem Solving
38. a.
33. 26 serves
f (x) 5 }}}
3
2
8
9
34. a. } 5 }
x
4.38 1 x
b. Skater 1: 39.42 km/h,
20.27x 3 1 1.4x 2 1 1.05x 1 39.4
28.25x 1 53.1x 2 7.82x 1 138
b. about $.29 per min
c. 2002
Skater 2: 35.04 km/h
c. About 0.23 h. Sample
answer: Divide the distance,
9 kilometers, by the rate,
39.42 kilometers per hour, to
find the time.
35. 1995
5
5
36. a. } room, }t room
8
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
5t 1 40
b. }; the expression
8t
represents the amount of
work done by you and your
friend while working together
for 5 hours.
3
5
1
c. }t 5 } l t 5 13} h; when
8
3
working together, you and
your friend can complete one
room.
}
1 1 Ï5
37. }
2
Algebra 2
Answer Transparencies for Checking Homework
178