Do you think the equations (x-1) (x+3) = 17+x and (x-1) (x+3) + 500=517+x should have the same solution set? Why?

Do you think the equations (x-1) (x+3) = 17+x and 3 (x-1) (x+3) = 51+3x should have the same solution set? Explain why.

Those two pair of equations have the same solution set.

Step-by-step explanation:

There are two equations

(x-1) (x+3) = 17+x ... (1) and

(x-1) (x+3) + 500=517+x ... (2)

We have to check the same solution set will be there for equations (1) and (2) or not.

Now, we are going to rearrange the equation (2).

(x-1) (x+3) + 500=517+x

⇒ (x-1) (x+3) = 517-500+x

⇒ (x-1) (x+3) = 17+x

This is the same equation as equation (1).

Therefore, there will be the same solution set for equations (1) and (2). (Answer)

There are two equations

(x-1) (x+3) = 17+x ... (3) and

3 (x-1) (x+3) + 500=51+3x ... (4)

We have to check the same solution set will be there for equations (3) and (4) or not.

Now, we are going to rearrange the equation (4).

3 (x-1) (x+3) + 500=51+3x

⇒ 3 (x-1) (x+3) = 3 (17+x)

⇒ (x-1) (x+3) = 17+x

This is the same equation as equation (3).

Therefore, there will be the same solution set for equations (3) and (4). (Answer)