Question

Given the equation 5+x−14=x−7.

Part A: Solve the equation 5+x−14=x−7. In your final answer, be sure to state the solution and include all of your work.

Part B: Use the values x=−2,0,3 to verify your solution to the equation 5+x−14=x−7. Include all of your calculations in the final answer.

Answer 1

Part A — Solve the equation

Start with
5 + x − 14 = x − 7.

Combine like terms on the left:
(5 − 14) + x = x − 7
−9 + x = x − 7
which we usually write as
x − 9 = x − 7.

Subtract x from both sides:
(x − 9) − x = (x − 7) − x
−9 = −7.

This is a false statement (−9 ≠ −7). Because the variable cancels and we are left with a contradiction, there is no value of x that satisfies the equation.

Solution: No solution (the solution set is ∅).

Part B — Verify using x = −2, 0, 3

1) x = −2:
Left: 5 + (−2) − 14 = 5 − 2 − 14 = −11.
Right: (−2) − 7 = −9.
−11 ≠ −9 → not a solution.

2) x = 0:
Left: 5 + 0 − 14 = −9.
Right: 0 − 7 = −7.
−9 ≠ −7 → not a solution.

3) x = 3:
Left: 5 + 3 − 14 = −6.
Right: 3 − 7 = −4.
−6 ≠ −4 → not a solution.

None of these values satisfy the equation, consistent with the conclusion that the equation has no solution.