Question

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 answer:

Choose 1 answer:


(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 answer:

Choose 1 answer:


(Choice A)

A

Yes


(Choice B)

B

No

Answer 1

Add/subtract the same quantity to/from both sides .... and yes

Step-by-step explanation:

got the answer from khan.

Answer 2

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

2) B. No

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:

`5x-2+x = x-4`

Add 2 to the left hand side of the equation

`5x-2+x+2 = x-4`

Simplify

`5x-2+2+x = x-4\\5x+0+x = x-4\\5x+x = x-4`

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:

`5x-2+x = x-4\\5x+x-2 = x-4\\6x-2 = x-4\\6x-x = -4+2\\5x = -2\\x = -2/5`

For equation B:

`5x+x = x-4\\5x+x-x = 4\\6x-x = 4\\5x = 4\\x= 4/5`

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