5.4: Error Analysis in Equations

• I can identify and correct an error in a given incorrect solution of a linear equation 

See if you can find the errors in this work. Then correct the mistake to solve for x.

We will return to these questions after the lesson to see how well you did. Feel free to edit your answers to reflect any new skills that can help you to find the error(s).

Think-Pair-Share

When solving equations, what are some of the common mistakes that you have made. 

Share with your desk partner.

Come up with a list of 3 possible mistakes that people might make.

Share the list with the class on a sticky-note and we will go through the list together.

Common Mistakes

❌ 1. Forgetting to do the same operation to both sides

🔍 Students sometimes apply an operation to one side only.

Incorrect:
x + 3 = 7

x + 3 - 3 = 8 Subtract 3 from left side only
❌x = 7 (no operation on right side)

Correct:
x + 3 = 7

 x  + 3 - 3 = 7 - 4 Subtract 3 from both sides 

x = 3✅

❌ 2. Incorrect use of inverse operations

🔍 Students add instead of subtract, or multiply when they should divide.

Example:
Incorrect: 

2x = 8

❌2x + 2 = 10 They add 2 instead of dividing
Correct:
2x = 8

(2x)/2 = 8 Divide both sides by 2

x = 4 ✅ 

❌ 3. Sign errors (positive/negative mistakes)

🔍 Students drop or change signs when moving terms.

Incorrect:
3x - 5 = 10

 ❌3x - 5 + 5 = 5 They add 5 but write 3x = 5
Correct:
3x - 5 = 10

3x - 5 + 5 = 10 + 5 Add 5 to both sides

 3x = 15 ✅

❌ 4. Distributing incorrectly

🔍 Students apply multiplication to only part of the expression.

Incorrect:
2(x + 3) = 10
❌ 2x + 3 = 10
Correct:
2(x + 3) = 10

2x + 2(3) = 10 Distribute to both terms

 2x + 6 = 10 ✅ 

❌ 5. Combining unlike terms

🔍 Students try to combine variables with constants.

Incorrect:
4x + 2 = 10

❌6x = 10 Added 4x and 2 to make 6x
Correct:
4x + 2 = 10

4x + 2 - 2 = 10 - 2 Only subtract the constant

4x = 8✅

❌6. Moving terms to the wrong side

🔍 When moving variables or constants, students often forget to change the sign.

Incorrect:
3x + 5 = x + 9

3x + 5 - x = 9 Move x without subtracting
❌4x + 5 = 9
Correct:
3x + 5 = x + 9

3x + 5 - x = x - x + 9 Subtract x 

2x + 5 = 9 ✅

❌ 7. Not checking the solution

🔍 Students finish solving but don’t verify by substitution.

Tip:

Always plug your answer back into the original equation to confirm. 

What steps can you take to ensure you are not making careless mistakes?

Error Analysis Questions in handout