Problem 1 · Check zero factors before canceling · 3 points
Made by AI and not reviewed by a real person.
What is the sum of all real values of x that make (x − 4)(x + 2) = (x − 4)(2x − 4) true?
- 4
- 10
- -2
- 6
- 2
Show a hint
- A matching expression on both sides is not always safe to cancel. What if it equals zero?
- Move everything to one side and factor before finding the solutions.
Show the answer and solution
Answer: B — 10
Subtract the right side to get (x − 4)[(x + 2) − (2x − 4)] = (x − 4)(6 − x) = 0. So x = 4 or x = 6, and their sum is 10. The tempting answer 6 comes from canceling x − 4 and losing the valid solution x = 4.