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.

Please show me your step by steps to get the answers so I can do it too with the rest of the questions, I really need to know how to do this. Thanks.

Answer 1

Part A:

Equation → 5 + x - 12 = x - 7

Combine Like Terms → -7 + x = x - 7

Subtract x to both sides → -7 + x - x = x - x - 7

Simplify → -7 = -7

Add 7 to both sides → -7 + 7 = -7 + 7

Simplify → 0 = 0

All real number are solutions.

Part B.

Using -4 for x.

5 + x - 12 = x - 7

5 + (-4) - 12 = -4 - 7

-11 = -11

Using 0 for x.

5 + x - 12 = x - 7

5 + 0 - 12 = 0 - 7

5 - 12 = -7

-7 = -7

Using 5 for x.

5 + x - 12 = x - 7

5 + 5 - 12 = 5 - 7

-2 = -2

Using all these numbers show that my original statement of "All real numbers are solutions" is correct.

Best of Luck!