Checking Solutions Examples in Math
Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Checking Solutions.
This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.
Concept Recap
Checking solutions means substituting candidate values back into the original condition to verify they satisfy it.
Treat your answer as a hypothesis and test it by substituting back into the original equation to verify.
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 candidate value is only a valid solution if substituting it makes the original equation or inequality true.
Common stuck point: Always check against the ORIGINAL equation, not a transformed version — transformed equations may have extra or fewer solutions.
Sense of Study hint: Always plug into the first equation given in the problem statement.
Worked Examples
Example 1
easySolution
- 1 Substitute x = 5 into the left side: 2(5) - 3 = 10 - 3 = 7.
- 2 Compare with right side: 7 = 7 ✓
- 3 Yes, x = 5 is a solution.
Answer
Example 2
mediumPractice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
easyExample 2
mediumRelated Concepts
Background Knowledge
These ideas may be useful before you work through the harder examples.