Question

Given the equation 5+x−12=2x−7.

Part A: Solve the equation 5+x−12=2x−7.

In your final answer, be sure to state the solution and include all of your work.
Part B: Use the values x=−0.5,0,1 to verify your solution to the equation 5+x−12=2x−7.

In your final answer, include all of your calculations. WRITER

Answer 1

Part A — Solve 5 + x − 12 = 2x − 7

1. Combine like terms on the left: 5 + x − 12 = x − 7, so the equation becomes
x − 7 = 2x − 7.

2. Subtract x from both sides:
x − 7 − x = 2x − 7 − x → −7 = x − 7.

3. Add 7 to both sides:
−7 + 7 = x − 7 + 7 → 0 = x.

Solution: x = 0.

Part B — Verify using x = −0.5, 0, 1

Compute left side L = 5 + x − 12 and right side R = 2x − 7 for each x.

- For x = −0.5:
L = 5 + (−0.5) − 12 = 5 − 0.5 − 12 = 4.5 − 12 = −7.5.
R = 2(−0.5) − 7 = −1 − 7 = −8.
L ≠ R (−7.5 ≠ −8), so x = −0.5 is not a solution.

- For x = 0:
L = 5 + 0 − 12 = 5 − 12 = −7.
R = 2(0) − 7 = 0 − 7 = −7.
L = R (−7 = −7), so x = 0 is a solution.

- For x = 1:
L = 5 + 1 − 12 = 6 − 12 = −6.
R = 2(1) − 7 = 2 − 7 = −5.
L ≠ R (−6 ≠ −5), so x = 1 is not a solution.

Conclusion: The equation 5 + x − 12 = 2x − 7 has the single solution x = 0, which is confirmed by the verification.