Solution Set Examples in Math

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

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 complete set of all values that satisfy a given equation or inequality — it may be empty, finite, or infinite.

Not just one answer, but ALL answers that work — an inequality like x > 3 has infinitely many.

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: Some equations have no solutions, one solution, or infinitely many.

Common stuck point: Don't forget negative solutions, or that inequalities have ranges.

Sense of Study hint: Ask yourself: could there be negative solutions? Fractional solutions? More than one solution?

Worked Examples

Example 1

easy
What is the solution set of x^2 = 25?

Solution

  1. 1
    Find all values where x^2 = 25: x = 5 or x = -5.
  2. 2
    Write as a set: \{5, -5\}.
  3. 3
    The solution set contains every value that satisfies the equation.

Answer

\{-5, 5\}
A solution set is the collection of all values that make the equation true. It can contain zero, one, two, or infinitely many elements.

Example 2

medium
What is the solution set of x + 3 > 5?

Practice Problems

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

Example 1

easy
What is the solution set of 2x = 10?

Example 2

medium
What is the solution set of x^2 + 1 = 0 over the real numbers?
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Background Knowledge

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

solution concept