AnswersNC-Foundations of Math 1 Fall 1st 9 WeeksSolving with Variables on Both Sides

Analyzing Solutions Answers

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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?

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

Trina examined the equation below and said that the equation has exactly one solution.Which explains whether Trina is correct?

Question illustration
A
Trina is correct because the two sides of the equation are equivalent.
B
Trina is correct because the two sides of the equation are not equivalent.
C
Trina is not correct because the two sides of the equation are equivalent.
D
Trina is not correct because the two sides of the equation are not equivalent.
4

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
3 (x + 4)
Option A
B
2 (x + 6) + x
Option B
C
4(x – 3) – x
D
3 (x + 1) + 9 x
Option D
5

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

Question illustration
A
–8
B
0
C
no solution
D
infinitely many solutions
6

Maria solved an equation as shown below.What is the solution to Maria’s equation?

Question illustration
A
19
B
38
C
no solution
D
infinitely many solutions
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 expression on the left side of an equation is shown below.If the equation has an infinite number of solutions, which expression can be written in the box on the other side of the equation?

Question illustration
A
Negative 5 (x minus 3) + 2 x
Option A
B
–5x – 10
C
x
Option C
D
Negative 2 (x + 5)
Option D
10

Zahra wants the equation below to have an infinite number of solutions when the missing number is placed in the box.Which number should she place in the box?

Question illustration
A
–3
B
–1
C
1
D
3

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