Verification of a linear equation means substituting a proposed value for the variable into the original equation and determining whether both sides have equal values; equality confirms that the value is in the solution set, while inequality rejects it. This applies to one-variable equations with integer or rational coefficients, including parentheses and fractions, and distinguishes checking a solution from merely obtaining an answer through algebraic manipulation; systems and nonlinear equations are beyond this scope.
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Detailed Explanation: Verify solutions to linear equations
To verify a proposed solution, substitute the value for the variable in the original equation. Then calculate both sides separately.
Suppose we want to check whether solves
Step 1: Substitute for .
Step 2: Simplify the left side.
Step 3: Compare both sides.
Both sides equal , so the equation is true. Therefore, is a solution.
If the two sides had different values, the equation would be false, and the proposed value would not be a solution.
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Verify a Solution to a Linear Equation - Single Equation to True or False
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- 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