Analyzing Solutions Answers

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Which statements accurately describe this equation? Check all that apply.

A
This equation has one solution.
B
This equation has no solution.
C
This equation has infinitely many solutions.
D
Any input value for the variable will generate a true equation.
E
Any input value for the variable will generate a false equation.
3

This equation has one solution✔ infinitely many solutionsno solution.

A
one solution
B
✔ infinitely many solutions
C
no solution
4

Which of the following is true? (Check all that apply.)

A
It is a true statement.
B
Any input will result in an equivalent equation.
C
It is equivalent to an equation of the form a = a.
D
It has no solution.
E
Only one input will result in a true statement.
5

Which linear equations have one solution? Check all that apply.

A
5x – 1 = 3(x + 11)
B
4(x – 2) + 4x = 8(x – 9)
C
4(x – 6) + 4 = 2(x – 3)
D
2(x – 4) = 5(x – 3) + 3
E
2(x – 1) + 3x = 5(x – 2) + 3
6

Which equation has infinitely many solutions?

A
5(2x + 4) = 10x – 12
B
5(2x + 4) = 10(x + 2)
C
5(2x + 4) = 12x
D
5(2x + 10) = 20(x + 1)
7

How many solutions does this equation have?

A
one solution
B
two solutions
C
infinitely many solutions
D
no solution
8

He used the distributive property incorrectly in the first step.He used the addition property of equality incorrectly in the second step.He should have found that the equation has one solution of x = 18.He should have found that there are no solutions because the statement is false.

A
He used the distributive property incorrectly in the first step.
B
He used the addition property of equality incorrectly in the second step.
C
He should have found that the equation has one solution of x = 18.
D
He should have found that there are no solutions because the statement is false.
9

Explain how to create an equation with infinitely many solutions.

Answer:

To create an equation with infinitely many solutions, start with a true statement such as a = a. Then, add the same variable term to both sides of the equation and add the same constant term to both sides. This ensures that both sides of the equation remain identical in value. When you combine like terms and simplify, both sides of the equals sign will be exactly the same, which means any value for the variable will make the equation true.

10

Sample Response: You can start with any statement in the form a = a. Then add the same variable term to both sides, and add the same constant term to both sides. Combine like terms on each side. Which did you include in your response? Check all that apply.Start with a statement in the form a = a.Add the same variable term to both sides.Add the same constant term to both sides.Combine like terms on each side.

A
Start with a statement in the form a = a.
B
Add the same variable term to both sides.
C
Add the same constant term to both sides.
D
Combine like terms on each side.

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