Find the error: two-step equations

A find-the-error worksheet for solving ax + b = c: undo the addition, then the multiplication. Each problem shows a student's worked solution with one planted mistake; students find the wrong step, name the misconception and solve it correctly. The answer key is computed, so it is always right.

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Divided only one side's term. Dividing by 5 first is allowed only if every term is divided: 5x + 25 = 40 would become x + 5 = 8. Easier: undo the + 25 first.Example: 5x + 25 = 40 worked to −17 instead of 3.
Used the wrong inverse operation on the constant. To undo + 18, subtract 18 from both sides.Example: 6y + 18 = 60 worked to 13 instead of 7.

Grade 7 · 7.EE.B.4a

Find the error: two-step equations

Name Date

Each problem was solved by a student, and each has exactly one mistake. Find the step with the mistake, say what went wrong, and solve the problem correctly.

1 6y + 18 = 60

Ana's work
1. Add 18 to both sides: 6y = 60 + 18 = 78.
2. Divide both sides by 6: y = 78 ÷ 6 = 13.
Ana's answer: 13

Wrong step: What went wrong: Correct answer:
2 5x + 25 = 40

Kai's work
1. Divide both sides by 5: x + 25 = 40 ÷ 5 = 8.
2. Subtract 25: x = −17.
Kai's answer: −17

Wrong step: What went wrong: Correct answer:
3 4x + 8 = 44

Rosa's work
1. Divide both sides by 4: x + 8 = 44 ÷ 4 = 11.
2. Subtract 8: x = 3.
Rosa's answer: 3

Wrong step: What went wrong: Correct answer:
4 2x − 2 = 6

Ivy's work
1. Subtract 2 from both sides: 2x = 6 − 2 = 4.
2. Divide both sides by 2: x = 4 ÷ 2 = 2.
Ivy's answer: 2

Wrong step: What went wrong: Correct answer:

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Answer key · Grade 7 · 7.EE.B.4a

Find the error: two-step equations

#	Wrong step	The mistake	Correct answer
1	Step 1	Used the wrong inverse operation on the constant. To undo + 18, subtract 18 from both sides.Correct step 1: Subtract 18 from both sides: 6y = 60 − 18 = 42.	7not 13
2	Step 1	Divided only one side's term. Dividing by 5 first is allowed only if every term is divided: 5x + 25 = 40 would become x + 5 = 8. Easier: undo the + 25 first.Correct step 1: Subtract 25 from both sides: 5x = 40 − 25 = 15.	3not −17
3	Step 1	Divided only one side's term. Dividing by 4 first is allowed only if every term is divided: 4x + 8 = 44 would become x + 2 = 11. Easier: undo the + 8 first.Correct step 1: Subtract 8 from both sides: 4x = 44 − 8 = 36.	9not 3
4	Step 1	Used the wrong inverse operation on the constant. To undo − 2, add 2 to both sides.Correct step 1: Add 2 to both sides: 2x = 6 + 2 = 8.	4not 2

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