Balance Principle Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Balance Principle.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

The rule that any operation applied to one side of an equation must also be applied to the other side to preserve equality.

An equation is like a balanced scale—add weight to both sides equally.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Equations stay true when you perform the same operation on both sides.

Common stuck point: Must apply the operation to the entire side, not just one term: 2x + 3 = 7 \ \Rightarrow \ 2x = 4 (subtract 3 from both sides).

Sense of Study hint: Write the equation as a balance scale drawing, then show the same operation applied to both sides.

Worked Examples

Example 1

easy
Solve \(x + 7 = 15\) using the balance principle.

Solution

  1. 1
    An equation is like a balance scale — both sides must stay equal.
  2. 2
    To isolate \(x\), subtract 7 from both sides.
  3. 3
    \(x + 7 - 7 = 15 - 7\).
  4. 4
    \(x = 8\).
  5. 5
    Check: \(8 + 7 = 15\) ✓

Answer

\(x = 8\)
The balance principle: whatever you do to one side, do to the other. Subtract 7 from both sides to keep the equation balanced.

Example 2

medium
Solve \(3x - 4 = 14\) using the balance principle, showing all steps.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
Solve \(n - 9 = 6\) using the balance principle.

Example 2

medium
Solve \(\frac{x}{4} + 3 = 10\).
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Background Knowledge

These ideas may be useful before you work through the harder examples.

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