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Verify solutions to equations by substitution

A solution to an equation is a value that makes the equation true when substituted for the variable in every occurrence, so verification requires evaluating both sides using order of operations and checking that their values are equal. This applies to linear equations with rational numbers, including negative numbers and fractions, and reinforces equality as a relationship rather than merely an answer produced by a procedure.

Detailed Explanation: Verify solutions to equations by substitution

To verify a solution, substitute the given value for the variable everywhere it appears. Then evaluate both sides using the order of operations. If both sides have the same value, the solution is correct.

Example: Verify whether x=−34x=-\frac34 is a solution to

4x+5=24x+5=2
  1. Substitute −34-\frac34 for xx:
4(−34)+5=24\left(-\frac34\right)+5=2
  1. Evaluate the multiplication first:
−3+5=2-3+5=2
  1. Simplify the left side:
2=22=2

Both sides are equal, so x=−34x=-\frac34 is a solution to the equation.

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