Question

For the equations given below, which statement is true?

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.

Step-by-step 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:

$-3x-8=19\\\\-3x=19+8\\\\x=\frac{27}{-3}\\\\x=-9$

- Second equation:

$-3x-2=25\\\\-3x=25+2\\\\x=\frac{27}{-3}\\\\x=-9$