Common Mistakes
Identify and avoid typical errors with linear equations.
Learn
Common Errors
- Sign errors: Forgetting to change signs when moving terms
- Distribution errors: Not distributing to all terms in parentheses
- Order of operations: Doing operations in wrong order
- Combining unlike terms: Adding 2x + 3 to get 5x is wrong
- Division errors: Dividing only part of the equation
Practice
Question 1: Find the error: x + 5 = 12, so x = 12 + 5 = 17.
Answer
Error: Should subtract 5, not add. Correct: x = 12 - 5 = 7.
Question 2: Find the error: 2(x + 3) = 10 becomes 2x + 3 = 10.
Answer
Error: Did not distribute to both terms. Correct: 2x + 6 = 10.
Question 3: Find the error: 3x - 2 = 7, so 3x = 5.
Answer
Error: Subtracted 2 instead of adding. Correct: 3x = 7 + 2 = 9, so x = 3.
Question 4: Find the error: 4x = 20, so x = 20 - 4 = 16.
Answer
Error: Should divide, not subtract. Correct: x = 20/4 = 5.
Question 5: Simplify correctly: 5x + 3 - 2x + 7
Answer
Combine like terms: 5x - 2x = 3x; 3 + 7 = 10. Answer: 3x + 10.
Question 6: Find the error: -3(x - 4) = -3x - 12.
Answer
Error: -3 times -4 equals +12, not -12. Correct: -3x + 12.
Question 7: Solve correctly: 2x/3 = 8.
Answer
Multiply both sides by 3: 2x = 24. Divide by 2: x = 12.
Question 8: Find the error: x/2 + 3 = 7 becomes x + 3 = 14.
Answer
Error: Should subtract 3 first, then multiply. Correct: x/2 = 4, so x = 8.
Question 9: Solve: -x = 5. What is x?
Answer
x = -5. Remember: -x means -1 times x. Divide both sides by -1.
Question 10: Check: Is x = 4 a solution to 2x - 3 = 5?
Answer
Check: 2(4) - 3 = 8 - 3 = 5. Yes, x = 4 is correct.