Equations Examples in Math

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

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

Concept Recap

A statement that two expressions are equal, often containing unknown values to find.

A balanced scale: both sides must weigh the same. Solve by keeping balance.

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 state equality; solving means finding values that make it true.

Common stuck point: Whatever operation you do to one side must be done to the other side — otherwise the equation is no longer balanced.

Sense of Study hint: Try covering the variable with your finger and asking: what number makes both sides the same?

Worked Examples

Example 1

easy
Is x = 4 a solution of 2x - 3 = 5?

Solution

  1. 1
    Substitute x = 4 into the left side: 2(4) - 3 = 8 - 3 = 5.
  2. 2
    Compare with the right side: 5 = 5 ✓.
  3. 3
    Since both sides are equal, x = 4 is a solution.

Answer

Yes, x = 4 is a solution.
An equation asserts that two expressions are equal. A value is a solution if substituting it makes both sides equal. Always check by plugging the value back in.

Example 2

medium
Solve \frac{x}{4} + 3 = 7.

Practice Problems

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

Example 1

easy
Solve x + 9 = 15.

Example 2

hard
Which of these is an equation and which is an expression? (a) 3x + 7 (b) 3x + 7 = 19
← Back to Equations Formula Explained Practice Mode

Background Knowledge

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

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