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Verify solutions to equations

A solution to an equation is a value that makes the original equality true when substituted for the variable. Verification involves evaluating both sides, including expressions with rational numbers, parentheses, and variables on either side, and determining whether they are equal; this distinguishes a valid solution from an arithmetic or algebraic error and supports reliable solution of linear equations. Nonlinear equations and systems are outside this scope.

Detailed Explanation: Verify solutions to equations

To verify a solution, substitute the given value for the variable into the original equation. Then evaluate the left side and right side separately. If they are equal, the value is a solution.

Example: Verify whether x=42x=42 is a solution to

2(x3−1)=x2+5.2\left(\frac{x}{3}-1\right)=\frac{x}{2}+5.
  1. Substitute 4242 for xx:
2(423−1)=422+5.2\left(\frac{42}{3}-1\right)=\frac{42}{2}+5.
  1. Evaluate the left side:
2(14−1)=2(13)=26.2(14-1)=2(13)=26.
  1. Evaluate the right side:
21+5=26.21+5=26.
  1. Compare the results:
26=26.26=26.

The two sides are equal, so x=42\boxed{x=42} is a solution to the original equation.

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