What you’ll learn
Recognize when equivalent steps lead to a false statement and an equation has no solution.
Key idea
When equal variable terms cancel and leave a false equality, no value of x can satisfy the original equation. For example, a statement such as 2 = 5 is false for every x.
Worked example
Solve. Show equivalent steps or enter No solution / All real numbers.
(6)x + (30) = (33) + (6)x
- (6)x + (30) = (6)x + (33)
- 30 = 33
Answer: No solution
Quick Check
Analyze the proposed student response. Choose Correct or Incorrect.
7(x + (-5)) = (7)x + (-32) Student response: No solution