Final answer:
After distributing and combining like terms, we find that the variable terms cancel each other out, leaving us with an untrue statement, -8 = 16. Hence, the equation has no solution.
Step-by-step explanation:
To solve the equation 3(x - 5) + 7 = 5x - (2x - 7) + 9, we begin by expanding the terms and simplifying both sides of the equation:
- First, distribute the 3 into the parentheses: 3*x - 3*5 + 7 = 5x - 2x + 7 + 9.
- This simplifies to: 3x - 15 + 7 = 3x + 16.
- Combine like terms: 3x - 8 = 3x + 16.
- To isolate x, we would normally subtract 3x from both sides, but here, we see that the 3x terms cancel each other out, leaving -8 = 16, which is not a true statement.
- Therefore, the equation has no solution since the x terms cancel out, and we are left with a false statement.
Checking the answer helps us confirm that there's no possible value of x that will satisfy this equation because the final step yields a contradiction.