Checking Solutions
Also known as: verify solution, solution check
Grade 6-8
View on concept mapChecking solutions means substituting candidate values back into the original condition to verify they satisfy it. Checking solutions catches algebra errors and identifies extraneous solutions introduced by squaring or other operations.
Definition
Checking solutions means substituting candidate values back into the original condition to verify they satisfy it.
💡 Intuition
Treat your answer as a hypothesis and test it by substituting back into the original equation to verify.
🎯 Core Idea
A candidate value is only a valid solution if substituting it makes the original equation or inequality true.
Example
Notation
Substitution verification: evaluate LHS and RHS separately.
🌟 Why It Matters
Checking solutions catches algebra errors and identifies extraneous solutions introduced by squaring or other operations.
💭 Hint When Stuck
After finding a solution, substitute it back into the original equation (not a simplified version). Evaluate each side independently and verify they are equal. For equations involving radicals or rational expressions, always check for extraneous solutions.
Related Concepts
🚧 Common Stuck Point
Always check against the ORIGINAL equation, not a transformed version — transformed equations may have extra or fewer solutions.
⚠️ Common Mistakes
- Substituting the solution back into a simplified equation instead of the original equation
- Forgetting to check for extraneous solutions introduced by squaring both sides or clearing denominators
- Rounding intermediate steps and getting a result that does not exactly satisfy the equation
Frequently Asked Questions
What is Checking Solutions in Math?
Checking solutions means substituting candidate values back into the original condition to verify they satisfy it.
When do you use Checking Solutions?
After finding a solution, substitute it back into the original equation (not a simplified version). Evaluate each side independently and verify they are equal. For equations involving radicals or rational expressions, always check for extraneous solutions.
What do students usually get wrong about Checking Solutions?
Always check against the ORIGINAL equation, not a transformed version — transformed equations may have extra or fewer solutions.
Prerequisites
Cross-Subject Connections
How Checking Solutions Connects to Other Ideas
To understand checking solutions, you should first be comfortable with evaluation, solution concept and equivalence.