Grade: 9 Subject: Math (Algebra I) Unit: Linear Equations & Inequalities Lesson: 5 of 6 SAT: Algebra ACT: Math

Common Mistakes

Learning Objectives

In this lesson, you will learn to:

Find and correct the error in each problem. Click to reveal the answer.

Question 1: A student solved 3(x + 2) = 15 and got x = 3. Is this correct?

Answer: Correct!

Check: 3(3 + 2) = 3(5) = 15. The answer is verified.

Question 2: Error: -3x = 12, so x = 4. What's wrong?

Answer: x = -4, not 4

Explanation: When dividing by a negative number, the sign changes. -3x = 12 means x = 12/(-3) = -4.

Question 3: Error: 2(x - 3) = 2x - 3. What's wrong?

Answer: Should be 2x - 6

Explanation: Must distribute to ALL terms inside parentheses: 2(x) - 2(3) = 2x - 6.

Question 4: Error: x/2 + 3 = 7, multiply by 2: x + 3 = 14. What's wrong?

Answer: Should be x + 6 = 14

Explanation: Must multiply EVERY term by 2: (x/2)(2) + (3)(2) = (7)(2), giving x + 6 = 14.

Question 5: Error: If 5x - 3 = 2x + 6, then 3x - 3 = 6. What's wrong?

Answer: Correct so far!

Check: 5x - 2x = 3x, and the -3 stays. So 3x - 3 = 6, giving x = 3. Verify: 5(3)-3 = 12, 2(3)+6 = 12.

Question 6: Error: For 2x + 4 > 10, dividing by 2 gives x + 2 > 5. Is this correct?

Answer: Correct!

Explanation: Dividing by a positive number does not flip the inequality. x + 2 > 5 gives x > 3.

Question 7: Error: For -2x > 8, dividing by -2 gives x > -4. What's wrong?

Answer: Should be x < -4

Explanation: When dividing (or multiplying) an inequality by a negative number, you must FLIP the inequality sign.

Question 8: Error: -(x - 5) = -x - 5. What's wrong?

Answer: Should be -x + 5

Explanation: Distribute the negative: -(x) - (-5) = -x + 5. Remember: negative times negative equals positive.

Question 9: Error: 3x + 2x = 5x^2. What's wrong?

Answer: Should be 5x

Explanation: Adding like terms: 3x + 2x = 5x. Exponents only increase when multiplying: (3x)(2x) = 6x^2.

Question 10: Error: If 0x = 5, then x = 5. What's wrong?

Answer: No solution exists

Explanation: 0x = 0 for any value of x, so 0x can never equal 5. This equation has no solution.