Answer two questions about Equations AAA and BBB: \begin{aligned} A.&&5x&=3x B.&&5&=3 \end{aligned}

A.

B.





5x

5



=3x

=3



1) How can we get Equation BBB from Equation AAA?

Choose 1

Choose 1

(Choice A)

A

Add/subtract the same quantity to/from both sides

(Choice B)

B

Add/subtract a quantity to/from only one side

(Choice C)

C

Multiply/divide both sides by the same non-zero constant

(Choice D)

D

Multiply/divide both sides by the same variable expression

2) Based on the previous answer, are the equations equivalent? In other words, do they have the same solution?

Choose 1

Choose 1

(Choice A)

A

Yes

(Choice B)

B

No

1). A. Add/subtract a quantity to/from only one side  

2) B. No

Step-by-step explanation:

Given equation A

5x-2+x = x-4

Given equation B

5x+x = x-4

We can see that the difference between equation A and B is the 2 that subtracted from the left hand sides of the equation A. All other functions and constants remains the same.

For us to be able to get equation B from A, we need to simply add 2 to the left hand side of equation A to cancel out the -2 that is there as shown:

From equation A:

Add 2 to the left hand side of the equation

Simplify

We can see that the resulting function gives the equation B

Hence the option B is correct i.e Add/subtract a quantity to/from only one side  

Let us find the solution to equation A and B

For equation A:

For equation B:

Since we got different solution for x in both equation, hence both equation are not equivalent.