Subtracting before dividing in two-step equations
Undo the added number first, then divide by the coefficient.
The common mistake
Dividing first and only dividing one term — turning 3x + 5 = 20 into x + 5 = 20/3.
Instead: Undo operations in reverse order: subtract or add the constant first, then divide both sides by the number on x.
Worked example with Guide me
Solve 3x + 5 = 20.
- Sugar · What's being done to x, and in what order?Student · It's multiplied by 3, then 5 is added.
- Sugar · So what do we undo first? Subtract 5 from both sides — what's on the right?Student · 15, so 3x = 15.
- Sugar · Now undo the multiply. What is x?Student · 15 ÷ 3 = 5.
Answer: x = 5. Check: 3(5) + 5 = 20.
Try 3 practice questions
1. Solve 4x + 7 = 31.
Show answer
x = 6
2. Solve 5x − 3 = 22.
Show answer
x = 5
3. Solve 2x + 9 = 1.
Show answer
x = −4
Quick answers
- What is the most common mistake with subtracting before dividing in two-step equations?
- Dividing first and only dividing one term — turning 3x + 5 = 20 into x + 5 = 20/3.
- How do I get subtracting before dividing in two-step equations right?
- Undo operations in reverse order: subtract or add the constant first, then divide both sides by the number on x.
- Can you show a worked example?
- Solve 3x + 5 = 20. x = 5. Check: 3(5) + 5 = 20.
Related concepts
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