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Solve for the unknown (like x)

Imagine an equation is a balance scale. Whatever you do to one side, you must do to the other side so the scale stays balanced. The unknown (often called x) is a number that we need to find.

Step-by-step rules

  1. Find the unknown: Look for the variable (like x).
  2. Use inverse operations: To undo adding, subtract. To undo subtracting, add. To undo multiplying, divide. To undo dividing, multiply.
  3. Do the same to both sides: Whatever you do on one side of the =, do it on the other side too.
  4. Check by putting your answer back into the original equation.

Examples

1) x + 5 = 12

We want x alone. Undo +5 by subtracting 5 on both sides:

x + 5 - 5 = 12 - 5

x = 7

Check: 7 + 5 = 12 ✅

2) x - 4 = 9

Undo -4 by adding 4 on both sides:

x - 4 + 4 = 9 + 4

x = 13

Check: 13 - 4 = 9 ✅

3) 3x = 15

Here x is multiplied by 3. Undo ×3 by dividing both sides by 3:

3x ÷ 3 = 15 ÷ 3

x = 5

Check: 3 × 5 = 15 ✅

4) x / 4 = 6

Undo ÷4 by multiplying both sides by 4:

(x / 4) × 4 = 6 × 4

x = 24

Check: 24 ÷ 4 = 6 ✅

5) Two-step: 2x + 3 = 11

First undo +3 by subtracting 3 from both sides:

2x + 3 - 3 = 11 - 3 → 2x = 8

Now undo ×2 by dividing both sides by 2:

2x ÷ 2 = 8 ÷ 2 → x = 4

Check: 2×4 + 3 = 8 + 3 = 11 ✅

Quick tips

  • Always keep the equation balanced — do the same thing to both sides.
  • Work step by step. Don't try several things at once.
  • Check your answer by putting it back into the original equation.

Practice problems (try these)

  1. x + 6 = 10
  2. x - 7 = 5
  3. 4x = 20
  4. x / 5 = 3
  5. 3x + 2 = 11

Answers

  1. x = 4
  2. x = 12
  3. x = 5
  4. x = 15
  5. x = 3

If you want, give me one of your equations and I'll show you how to solve it step by step!


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