Equal Examples in Math

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

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

Concept Recap

Having exactly the same value or amount; the relationship expressed by the symbol = between two expressions.

Like a balanced scale—both sides weigh the same. If you add weight to one side, you must add to the other.

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: Equality is a relationship of sameness, not just 'the answer'.

Common stuck point: Thinking = means 'the answer is' instead of 'is the same as'.

Sense of Study hint: Try reading the equals sign as 'is the same amount as' and check: does the left side balance with the right side?

Worked Examples

Example 1

easy
Is the equation 3 + 4 = 8 - 1 true? Show why.

Solution

  1. 1
    Evaluate the left side: 3 + 4 = 7.
  2. 2
    Evaluate the right side: 8 - 1 = 7.
  3. 3
    Both sides equal 7, so the equation is true: 7 = 7.

Answer

\text{True: both sides equal } 7
The equals sign means both sides represent the same value, not that the left side produces the right side. Evaluating each side independently and comparing confirms equality. The equation is a balance, not a one-way computation.

Example 2

medium
Find the value of x that makes 2x + 3 = 11 true.

Practice Problems

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

Example 1

easy
Fill in the blank: 12 - 5 = \_ + 2.

Example 2

medium
Determine whether \frac{4}{6} = \frac{6}{9}. Justify your answer.
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Background Knowledge

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

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