Dividing both sides to isolate x
Divide the whole of each side by the coefficient on x.
The common mistake
Dividing only the x side, or dividing by the wrong number (e.g. subtracting 4 from 4x instead of dividing).
Instead: Whatever multiplies x, divide both sides by exactly that number — including its sign.
Worked example with Guide me
Solve −4x = 28.
- Sugar · What number is multiplying x?Student · −4.
- Sugar · Divide both sides by −4. What's 28 ÷ −4?Student · −7.
Answer: x = −7. Check: −4(−7) = 28.
Try 3 practice questions
1. Solve 6x = 42.
Show answer
x = 7
2. Solve −3x = 18.
Show answer
x = −6
3. Solve x/5 = 4.
Show answer
x = 20 (multiply both sides by 5)
Quick answers
- What is the most common mistake with dividing both sides to isolate x?
- Dividing only the x side, or dividing by the wrong number (e.g. subtracting 4 from 4x instead of dividing).
- How do I get dividing both sides to isolate x right?
- Whatever multiplies x, divide both sides by exactly that number — including its sign.
- Can you show a worked example?
- Solve −4x = 28. x = −7. Check: −4(−7) = 28.
Related concepts
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Save this as a miss — practice it before your test