What you’ll learn
Recognize when both sides simplify identically and every real number is a solution.
Key idea
If simplifying both sides leaves the same expression, the equation is true for every real value of x. A true statement such as 5 = 5 places no restriction on x, so there are infinitely many solutions.
Worked example
Solve. Show equivalent steps or enter No solution / All real numbers.
(6)x + (30) = (30) + (6)x
- (6)x + (30) = (6)x + (30)
- 30 = 30
Answer: All real numbers
Quick Check
Analyze the proposed student response. Choose Correct or Incorrect.
7(x + (-5)) = (7)x + (-35) Student response: All real numbers