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Analyzing Solutions Answers

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Jubal wrote the four equations below. He examined them, without solving them, to determine which equation has no solution.Which of Jubal’s equations has no solution?

Question illustration
A
7 x + 1 = 7 x+ 1
Option A
B
3 x + 2 = 3 x minus 2
Option B
C
4 x + 1 = 3 x + 8
Option C
D
negative 2 x minus 1 = negative 2 x minus 1
Option D
2
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The expression on the left side of an equation is shown below.If the equation has no solution, which expression can be written in the box on the other side of the equation?

Question illustration
A
2(x + 4) – x
B
x + 8
C
4(x + 2) – 5x
D
x
3

Jeremy wants to determine the number of solutions for the equation below without actually solving the equation.Which method should Jeremy use?

Question illustration
A
Determine whether the equation has the form , and if it does, the equation has infinitely many solutions.
Option A
B
Determine whether the equation has the form , and if it does, the equation has no solution.
Option B
C
Determine whether the equation has the form , and if it does, the equation has one solution.
Option C
D
Determine whether the equation has the form , and if it does, the equation has no solution.
Option D
4

Dante wrote several equations and determined that only one of the equations has infinitely many solutions. Which of these equations has infinitely many solutions?

A
6 (x + 3) + x = 7 x + 2 + 1
Option A
B
6 (x + 3) + x = 7 x + 5
Option B
C
6 (x + 3) + x = 6 x + 3 + 15
Option C
D
6 (x + 3) + x = 7 x + 9 + 9
Option D
5

Yuto solved the equation below.What is the solution to Yuto’s equation?

Question illustration
A
–10
B
9
C
no solution
D
infinitely many solutions
6

Candice wrote the four equations below. She examined them, without solving them, to determine which equation has an infinite number of solutions.Which of Candice’s equations has an infinite number of solutions?

Question illustration
A
Negative 5 x + 1 = negative 5 x + 1
Option A
B
Negative 2 x + 1 = negative 2 x + 2
Option B
C
3 x + 5 = 3 x minus 5
Option C
D
4 x minus 2 = x + 1
Option D
7

Leonardo wrote an equation that has an infinite number of solutions. One of the terms in Leonardo’s equation is missing, as shown below.Which could be the missing term that Leonardo put into the box?

Question illustration
A
x
B
3x
C
1
D
5
8

LaShawn solved the equation below to the determine the solution.How many solutions does LaShawn’s equation have?

Question illustration
A
zero
B
one
C
two
D
infinitely many
9

The equation below has one solution.What is the solution to the equation?

Question illustration
A
–2
B
–1
C
1
D
2
10

Chelsea wrote several equations and determined that only one of the equations has exactly one solution. Which of these equations has exactly one solution?

A
4 (x + 3) = 7 x minus 6
Option A
B
4 (x + 3) + 8 = 4 x + 20
Option B
C
4 (x + 3) + 3 x + 7 x + 12
Option C
D
4 (x + 3) + 6 = 4 x + 9
Option D

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Analyzing Solutions Answers — Math 8