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About this video
Equations where x sits in the denominator, solved with one simple trick: write the other side as a fraction over 1, then swap the denominator with the number across the equal sign. Three worked examples, ending with a two-term denominator.
What it covers
- Writing a whole number as a fraction over 1
- The swap: the denominator changes places with the number across the equal sign
- A denominator with two terms, such as 2x + 1, moves as one piece
- Finishing with inverse operations, then checking the answer
Extra worked examples
✍️ Extra example: solve 18/x = 6
- 1Write 6 as a fraction: 18/x = 6/1.Every whole number is itself over 1.
- 2Swap the x and the 6: 18/6 = x.The denominator changes places with the number on the other side of the equal sign.
- 3x = 3.18 ÷ 6 = 3. Check: 18/3 = 6 ✓
✍️ Extra example: solve 20/(x − 1) = 4
- 1Swap the whole denominator with the 4: 20/4 = x − 1.A two-term denominator moves as one piece, exactly like a single letter.
- 25 = x − 1.20 ÷ 4 = 5.
- 35 + 1 = x, so x = 6.The inverse of − 1 is + 1 on the other side.
- 4Check: 20/(6 − 1) = 20/5 = 4 ✓Substitute the answer back into the question.
Exercises to try
Work each one out, then click to reveal the answer.
- 1Solve 12/x = 4.
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12/4 = x, so x = 3 - 2Solve 35/x = 7.
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35/7 = x, so x = 5 - 3Solve 24/(x + 2) = 6.
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24/6 = x + 2 → 4 = x + 2 → x = 2 - 4Solve 30/3x = 5.
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30/5 = 3x → 6 = 3x → x = 2 - 5Solve 14/(2x + 1) = 4.
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14/4 = 2x + 1 → 3,5 = 2x + 1 → 2,5 = 2x → x = 1,25
