AnswersPBCSD_Grade_Forgiveness_1200330_Algebra 2_S2_2024Rational Equations

Rational Equations Answers

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1
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What is the solution to the equation ?

Question illustration
A
m = 3
B
m = 6
C
all real numbers
D
no solution
2
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What are the solutions to the equation

Question illustration
A
x = –7 and x = 1
B
x = –6 and x = –1
C
x = –1 and x = 7
D
x = 1 and x = 6
3

Which solution to the equation is extraneous?

Question illustration
A
g = –4
B
g = –4 and g = 16
C
neither g = –4 nor g = 16
D
g = 16
4

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?

Question illustration
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.
5

What is the solution to the equation ?

Question illustration
A
d = –4 and d = 2
B
d = –2 and d = 4
C
d = 1
D
d = 2
6

What are the solutions to the equation ?

Question illustration
A
w = –6 and w = –2
B
w = 0, w = 2, and w = 6
C
w = 0 and w =
Option C
D
w = 2 and w = 6
7

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

Question illustration
A
y
B
y2 – 1
C
y + 1
D
y2 + y + 2
8

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?

Question illustration
A
1 hour 20 minutes
B
3 hours 20 minutes
C
4 hours
D
6 hours
9

A contractor has two choices for billing a completed job. · $500 flat rate, regardless of the number of hours worked· $20 per hour workedThe graph shows the relationship between pay per hour and number of hours worked for both scenarios. What is the solution to this system of equations, and what does it mean to the contractor?

Question illustration
A
The solution (0, 20) tells the contractor the minimum amount that can be charged.
B
The solution (0, 500) tells the contractor the maximum amount that can be charged.
C
The solution (25, 20) tells the contractor the number of hours on a job where the hourly rate is the same for both billing options.
D
The solution (20, 25) tells the contractor the number of hours on a job where the hourly rate is the same for both billing options.
10

What is true about the solution of ?

Question illustration
A
, and they are actual solutions.
Option A
B
, but they are extraneous solutions.
Option B
C
x = 3, and it is an actual solution.
D
x = - 3, but it is an extraneous solution.

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