Rational Equations Answers

1

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Which solution to the equation is extraneous?

A

x = 1 and x = –4

B

neither x = 1 or x = –4

C

x = 1

D

x = –4

1

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What causes a solution to a rational equation to be an extraneous solution?

A

When there is more than one solution, one of the solutions is extraneous.

B

If a solution results in zero when substituted into the denominator of the equation, the solution is extraneous.

C

If a solution results in a negative number when substituted into the denominator of the equation, the solution is extraneous.

D

When a solution is a fraction, the solution is extraneous.

1

Which solution to the equation is extraneous?

A

g = –4

B

g = –4 and g = 16

C

neither g = –4 nor g = 16

D

g = 16

1

What is the solution of ?

A

y = –4

B

y = –2

C

y = 4

D

y = 6

2

What is true about the solution of ?

A

, and they are actual solutions.

B

, but they are extraneous solutions.

C

x = 3, and it is an actual solution.

D

x = - 3, but it is an extraneous solution.

2

What is the solution to the equation ?

A

m = 3

B

m = 6

C

all real numbers

D

no solution

2

What is the solution to the equation ?

A

d = –4 and d = 2

B

d = –2 and d = 4

C

d = 1

D

d = 2

3

Which of the following represents the solution of ?

A

x = one-fifth

B

x = five-ninths

C

all real numbers

D

no solution

3

Which of the following represents the solution of ?

A

x = one-fifth

B

x = five-ninths

C

all real numbers

D

no solution

4

What is the solution to the equation ?

A

d = –4 and d = 2

B

d = –2 and d = 4

C

d = 1

D

d = 2

4

Which solution to the equation is extraneous?

A

x = 1 and x = –4

B

neither x = 1 or x = –4

C

x = 1

D

x = –4

5

Working alone, it would take Shandra 40 minutes to sand a table. To sand the same table, also working alone, it would take Kelly 1 hour. If they work together, the situation can be modeled by the following equation, where t is the time it would take to sand the table working together.Shandra claims it will take them about 50 minutes working together, because 50 is the mean of 40 and 60. Which best describes Shandra’s claim?

A

Shandra’s claim is correct.

B

Shandra’s estimate is too high because she should have found the differences instead of the mean.

C

Shandra’s estimate is too high because it will take them about 24 minutes.

D

Shandra’s estimate is too low because it will take them about 100 minutes.

5

Consider the graph showing two functions. Which answer can be used to find the solution to the system of equations?

A

mc030-2.jpg

B

mc030-3.jpg

C

mc030-4.jpg

D

mc030-5.jpg

5

What is true about the solution of ?

A

, and they are actual solutions.

B

, but they are extraneous solutions.

C

x = 3, and it is an actual solution.

D

x = - 3, but it is an extraneous solution.

6

What is the solution for the equation ?

A

b = –4 and b = 0

B

b = –4

C

b = 0 and b = 4

D

b = 4

6

What are the solutions to the equation ?

A

w = –6 and w = –2

B

w = 0, w = 2, and w = 6

C

w = 0 and w =

D

w = 2 and w = 6

6

What is the solution to the equation ?

A

h = eleven-thirds

B

h = 5

C

h = 7

D

h = twenty-one-halves

7

What are the solutions to the equation

A

x = –7 and x = 1

B

x = –6 and x = –1

C

x = –1 and x = 7

D

x = 1 and x = 6

7

Kent multiplies both sides of the equation below by an expression.Then he moves all the terms to one side of the equal sign in the resulting equation. Which equation must he solve now?

A

k squared minus 8 k minus 12 = 0

B

k squared + 8 k + 12 = 0

C

k squared minus 8 + 12 = 0

D

k squared minus 8 k + 12 = 0

7

Yumi and Juan pick up litter along the highway at the same rate. Yumi picks up litter for 3 miles and takes 2 hours longer than Juan, who picks up litter for 2 miles. If Juan spent x hours picking up litter, the following equation models the situation.How long did Yumi spend picking up litter?

A

1 hour 20 minutes

B

3 hours 20 minutes

C

4 hours

D

6 hours

8

A student solves the following equation for all possible values of x:His solution is as follows: Step 1: 8(x – 4) = 2(x + 2)Step 2: 4(x – 4) = (x + 2)Step 3: 4x – 16 = x + 2Step 4: 3x = 18Step 5: x = 6He determines that 6 is an extraneous solution because the difference of the numerators is 6, so the 6s cancel to 0.Which best describes the reasonableness of the student’s solution?

A

His solution for x is correct and his explanation of the extraneous solution is reasonable.

B

His solution for x is correct, but in order for 6 to be an extraneous solution, both denominators have to result in 0 when 6 is substituted for x.

C

His solution for x is correct, but in order for 6 to be an extraneous solution, one denominator has to result in 0 when 6 is substituted for x.

D

His solution for x is incorrect. When solved correctly, there are no extraneous solutions.

8

Consider the graph showing two functions. Which answer can be used to find the solution to the system of equations?

A

mc030-2.jpg

B

mc030-3.jpg

C

mc030-4.jpg

D

mc030-5.jpg

9

What is the solution of ?

A

y = –4

B

y = –2

C

y = 4

D

y = 6

9

Yumi and Juan pick up litter along the highway at the same rate. Yumi picks up litter for 3 miles and takes 2 hours longer than Juan, who picks up litter for 2 miles. If Juan spent x hours picking up litter, the following equation models the situation.How long did Yumi spend picking up litter?

A

1 hour 20 minutes

B

3 hours 20 minutes

C

4 hours

D

6 hours

9

Kent multiplies both sides of the equation below by an expression.Then he moves all the terms to one side of the equal sign in the resulting equation. Which equation must he solve now?

A

k squared minus 8 k minus 12 = 0

B

k squared + 8 k + 12 = 0

C

k squared minus 8 + 12 = 0

D

k squared minus 8 k + 12 = 0

10

Janet wants to solve the equation . What should she multiply both sides of the equation by?

A

y

B

y2 – 1

C

y + 1

D

y2 + y + 2

10

A student solves the following equation for all possible values of x:His solution is as follows: Step 1: 8(x – 4) = 2(x + 2)Step 2: 4(x – 4) = (x + 2)Step 3: 4x – 16 = x + 2Step 4: 3x = 18Step 5: x = 6He determines that 6 is an extraneous solution because the difference of the numerators is 6, so the 6s cancel to 0.Which best describes the reasonableness of the student’s solution?

A

His solution for x is correct and his explanation of the extraneous solution is reasonable.

B

His solution for x is correct, but in order for 6 to be an extraneous solution, both denominators have to result in 0 when 6 is substituted for x.

C

His solution for x is correct, but in order for 6 to be an extraneous solution, one denominator has to result in 0 when 6 is substituted for x.

D

His solution for x is incorrect. When solved correctly, there are no extraneous solutions.

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