Checking Solutions

Algebra
process

Also known as: verify solution, solution check

Grade 6-8

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Checking 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

x = 3 \text{ in } 2x+1=7: \quad 2(3)+1 = 7 \checkmark — left side equals right side.

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

Always plug into the first equation given in the problem statement.

🚧 Common Stuck Point

Always check against the ORIGINAL equation, not a transformed version — transformed equations may have extra or fewer solutions.

⚠️ Common Mistakes

  • Stopping after isolation without substitution
  • Accepting extraneous roots from squaring steps

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.

Why is Checking Solutions important?

Checking solutions catches algebra errors and identifies extraneous solutions introduced by squaring or other operations.

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.

What should I learn before Checking Solutions?

Before studying Checking Solutions, you should understand: evaluation, solution concept, equivalence.

How Checking Solutions Connects to Other Ideas

To understand checking solutions, you should first be comfortable with evaluation, solution concept and equivalence.

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