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Solutions for Quiz 9 - Elementary Algebra | MTH 092, Quizzes of Algebra

Material Type: Quiz; Professor: Bannon; Class: Elementary Algebra; Subject: Mathematics; University: Essex County College; Term: Spring 2005;

Typology: Quizzes

Pre 2010

Uploaded on 08/08/2009

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MTH 092 Spring 2005
Essex County College Division of Mathematics
Quiz # 91 March 31, 2005
Name:
Signature:
Show all work clearly and in order, and box your final answers. Justify your answers algebraically
whenever possible. You have 20 minutes to take this 10 point quiz. No calculators or cellular
phones allowed. Do two of the following three problems.
1. Simplify. x
x+ 3 +2x1
x2+x6
Work: The LCM is (x+ 3) (x2).
x
x+ 3 +2x1
x2+x6=x
x+ 3 +2x1
(x+ 3) (x2)
=x
x+ 3 +2x1
(x+ 3) (x2)
=x
x+ 3
·
x2
x2+2x1
(x+ 3) (x2)
=x2
2x
(x+ 3) (x2) +2x1
(x+ 3) (x2)
=x2
1
(x+ 3) (x2)
2. Solve for x.x
x+ 3 +2x1
x2+x6= 0
Work: The LCM is (x+ 3) (x2).
x
x+ 3 +2x1
(x+ 3) (x2) = 0
(x+ 3) (x2) ·
x
x+ 3 + (x+ 3) (x2) ·
2x1
(x+ 3) (x2) = (x+ 3) (x2) ·0
(x2) ·x+ (2x1) = 0
x2
1=0
(x1) (x+ 1) = 0
1This document was prepared by Ron Bannon using L
A
T
E
X 2ε.
1
pf2

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MTH 092 — Spring — 2005 Essex County College — Division of Mathematics Quiz # 9^1 — March 31, 2005

Name:

Signature:

Show all work clearly and in order, and box your final answers. Justify your answers algebraically whenever possible. You have 20 minutes to take this 10 point quiz. No calculators or cellular phones allowed. Do two of the following three problems.

  1. Simplify. x x + 3
  • 2 x^ −^1 x^2 + x − 6

Work: The LCM is (x + 3) (x − 2). x x + 3

  • 2 x^ −^1 x^2 + x − 6

= x x + 3

  • 2 x^ −^1 (x + 3) (x − 2) = x x + 3

  • 2 x^ −^1 (x + 3) (x − 2) =

x x + 3 ·^

x − 2 x − 2 +^

2 x − 1 (x + 3) (x − 2)

= x

(^2) − 2 x (x + 3) (x − 2)

  • 2 x^ −^1 (x + 3) (x − 2)

= x

(x + 3) (x − 2)

  1. Solve for x.

x x + 3 +^

2 x − 1 x^2 + x − 6 = 0 Work: The LCM is (x + 3) (x − 2). x x + 3 +^

2 x − 1 (x + 3) (x − 2) =^0 (x + 3) (x − 2) · x x + 3

  • (x + 3) (x − 2) · 2 x^ −^1 (x + 3) (x − 2)

= (x + 3) (x − 2) · 0

(x − 2) · x + (2x − 1) = 0 x^2 − 1 = 0 (x − 1) (x + 1) = 0

(^1) This document was prepared by Ron Bannon using LATEX 2ε.

x = 1 or x = − 1

  1. A saltwater solution is formed by mixing 4 pounds of salt with 10 gallons of water. At this rate, how many additional pounds of salt are required for 15 gallons of water?

Work: The LCM is 30. 4 10

= 4 +^ x 15 30 · 104 = 30 · 4 + 15 x 12 = 8 + 2x 4 = 2 x 2 = x

Two additional pounds of salt are required.