Solution Concept Examples in Math

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

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 specific value (or set of values) that makes an equation or inequality true when substituted in for the variable.

The answer to 'what value of x makes this equation true?' — found by solving, confirmed by checking.

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: A solution satisfies the equation — substituting it back in makes both sides equal (it passes the test).

Common stuck point: Always verify: substitute your answer back into the original equation to confirm both sides are equal.

Sense of Study hint: Substitute your answer back into the original equation and verify both sides give the same number.

Worked Examples

Example 1

easy
Is x = 3 a solution of x^2 - 9 = 0?

Solution

  1. 1
    Substitute x = 3: (3)^2 - 9 = 9 - 9 = 0.
  2. 2
    Since the result is 0, x = 3 satisfies the equation.
  3. 3
    Therefore x = 3 is a solution.

Answer

Yes, x = 3 is a solution.
A solution is a value that, when substituted into the equation, makes the equation true. The verification process is called checking the solution.

Example 2

medium
Find all solutions of |x| = 5.

Practice Problems

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

Example 1

easy
Which values are solutions of x^2 = 16: x = 4, x = -4, x = 8?

Example 2

medium
Does the equation x + 1 = x + 2 have any solutions?
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Background Knowledge

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

equations