AnswersPBCSD_Grade_Forgiveness_1200330_Algebra 2_S2_2024Rational Equations

Rational Equations Answers

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1
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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
2
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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
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

How many extraneous solutions does the equation below have?

Question illustration
A
0
B
1
C
2
D
3
5

What is the solution to the equation ?

Question illustration
A
h = eleven-thirds
Option A
B
h = 5
Option B
C
h = 7
Option C
D
h = twenty-one-halves
Option D
6

Which of the following represents the solution of ?

Question illustration
A
x = one-fifth
Option A
B
x = five-ninths
Option B
C
all real numbers
D
no solution
7

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

Question illustration
A
mc030-2.jpg
Option A
B
mc030-3.jpg
Option B
C
mc030-4.jpg
Option C
D
mc030-5.jpg
Option D
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?

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.
9

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.
10

What is the solution of ?

Question illustration
A
y = –4
B
y = –2
C
y = 4
D
y = 6

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