Question

Given the equation 5 + x - 12 = x - 7. Part A. Solve the equation 5 + x - 12 = x - 7. In your final answer, be sure to state the solution and include all of your work. Part B. Use the values x = -4, 0, 5 to prove your solution to the equation 5 + x - 12 = x - 7. In your final answer, include all of your calculations.

Answer 1

Part A:
$5+x-12=x-7$
$5+x=x+5$
$5=5$

Since we know that, this equation has infinite solutions.

Part B:
$5+(-4)-12=(-4)-7$
$-11=11$
- This is with our solution.

$5+0-12=0-7$
$-7=-7$
- This is with our solution.

$5+5-12=5-7$
$-2=-2$
- This is with our solution.

- So, we just proved that 3 random values work, this means that this equation does indeed have infinite solutions.