Question

For the equations given below, which statement is true?

A. The equations have the same solution because the second equation can be obtained by subtracting 19 from both sides of the first equation.

B. The equations do not have the same solution because the second equation can be obtained by adding 6 to both sides of the first equation.

C. The equations have the same solution because the second equation can be obtained by adding 6 to both sides of the first equation.

D. The equations have the same solution because the second equation can be obtained by subtracting 6 from both sides of the first equation.

Answer 1

Answer: C. The equations have the same solution because the second equation can be obtained by adding 6 to both sides of the first equation.

Explanation:

You know that the first equation is:

`-3x-8=19`

And the second equation is:

`-3x-2=25`

According to the Addition property of equality:

If
`a=b`; then
`a+c=b+c`

Then, you can add 6 to both sides of the first equation to keep it balanced. Then, you get:

`-3x-8=19\\\\-3x-8+(6)=19+(6)`

`-3x-2=25`

Therefore, you can observe that the second equation can be obtained by adding 6 to both sides of the first equation, therefore, the equations have the same solution.

If you want to verify this, you can solve for "x" from both equations:

- First equation:

`-3x-8=19\\\\-3x=19+8\\\\x=(27)/(-3)\\\\x=-9`

- Second equation:

`-3x-2=25\\\\-3x=25+2\\\\x=(27)/(-3)\\\\x=-9`