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.
To verify whether a proposed value solves an equation:
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.
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