Skill: Verify algebraic solutions by substitution
Explanation and Free Practice Resources
Verification by substitution means replacing a variable with a proposed value everywhere it occurs, evaluating both sides of the equation, and determining whether the resulting equality is true. It distinguishes a value that satisfies the entire equation from one that only makes part of an expression appear correct, supporting reliable algebraic reasoning with one-variable equations involving whole numbers, integers, fractions, and decimals; systems, identities, and advanced extraneous-solution analysis are not included.
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Detailed Explanation: Verify algebraic solutions by substitution
To verify whether a proposed value solves an equation:
- Replace the variable with the proposed value everywhere it appears.
- Evaluate the left side.
- Evaluate the right side.
- Compare the results. If they are equal, the value is a solution.
Example: Check whether is a solution to
Substitute for :
Evaluate the left side:
The equation becomes
This statement is true, so is a solution to the equation.
Learn by doing: Verify algebraic solutions by substitution
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Practice:
Two-Step Equation - Subtraction and Division - Solve
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Download/Modify Free Grade 6 'Verify algebraic solutions by substitution' Worksheet
Print this free 'Verify algebraic 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:
- Two-Step Equation - Subtraction and Division - Solve
- Algebraic Function Variable Substitution - Simple Terms
- Algebraic Function Variable Substitution - Bracketed Terms
- Algebraic Functions - Variable Substitution to Equation - Bracketed Terms
- Algebraic Function Variable Substitution - Fractional Terms
- Algebraic Function Variable Substitution - Multiple Fractional Terms (Negatives)
- Subtraction - Missing Value, 2 Digit, 2 Numbers
- Fraction Subtraction - Missing Value (Mixed) - No Changed Denominator
Units Teaching This Skill
These adaptive units introduce, teach, or reinforce this skill (Verify algebraic solutions by substitution) through scaffolded problems that grow in difficulty as concepts are understood.