Substitution means replacing a variable in an equation with a proposed value, evaluating both sides according to the order of operations, and determining whether the resulting numerical statements are equal. This distinguishes a value that satisfies an equation from one that merely makes one side true and supports later reasoning about equivalent equations and algebraic solutions; the focus is on simple one-variable equations and does not include formal proof of identities, systems, or advanced symbolic verification.
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Detailed Explanation: Check solutions by substitution
To check whether a proposed value solves an equation, substitute it for the variable.
- Replace every variable with the proposed value.
- Evaluate each side using the order of operations.
- Compare the two answers. If they are equal, the value is a solution.
Example: Check whether is a solution to
Replace with :
Evaluate the left side:
Now compare both sides:
The two sides are equal, so is a solution to the equation.
Learn by doing: Check solutions by substitution
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Practice:
Verify a Solution to a Linear Equation - Single Equation to True or False
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Download/Modify Free Grade 6 'Check solutions by substitution' Worksheet
Print this free 'Check solutions by substitution' worksheet to practice this skill away from the computer. Click 'Modify' to easily customize this worksheet to your exact needs.
This Worksheet Includes:
- Verify a Solution to a Linear Equation - Single Equation to True or False
- Verify a Solution to a Linear Equation - Single Equation to Substituted Equation
- Linear Equation Systems - Simple Number Substitution To Equation
- Algebraic Function Variable Substitution - Simple Terms
Units Teaching This Skill
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