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Lesson 2 of 5

SHORTCUT

Change the side, change the sign

Move a term across the equals sign and flip what it does.

The question

Solve 3x − 4 = 11

The trick

Any term can cross the equals sign as long as it flips: plus becomes minus, times becomes divide.

Worked example

  1. 1Move the −4 across; it becomes +4: 3x = 11 + 4
  2. 23x = 15
  3. 3Move the ×3 across; it becomes ÷3: x = 15 ÷ 3
  4. 4x = 5

So: x = 5

Remember it like this

Crossing the equals sign is crossing a road — you always turn around when you get to the other side.

In the exam

Move the numbers first and the coefficient last. Doing it the other way round drags fractions through every line and creates chances to slip.

Why it works

It's the same as doing the opposite operation to both sides — transposing just skips writing the middle line. The equals sign stays balanced because you undo exactly what you moved.

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Try it yourself

0/4 correct
  • 1

    2x + 5 = 17. What is x?

  • 2

    5x − 8 = 27. What is x?

  • 3

    3x + 4 = 19. What is x?

  • 4

    7x − 2 = 33. What is x?