Question

Explain how to check a solution of an equation.

   Explain how to check a solution of an equation.

Beginning Algebra

Beginning Algebra

Margaret L. Lial,… 11th Edition

Chapter 2, Problem 4

Instant Answer

Solved by Expert Matt Gibson

06/18/2020

Step 1

Step 1: Assume that we have solved an equation and found the value of the variable, say $x = 3$. Show more…

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Explain how to check a solution of an equation.

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Key Concepts

Simplification

After substitution, simplifying both sides of the equation using algebraic operations ensures that any reductions or cancellations are correctly performed, confirming that the left-hand side equals the right-hand side.

Extraneous Solutions

Certain solving methods, especially those involving operations like squaring or taking roots, can introduce solutions that don’t satisfy the original equation. Checking solutions through substitution helps identify and eliminate these extraneous results.

Substitution

Substitution involves replacing the variable in the equation with the candidate solution to see if the resulting numerical statement is true. This technique is fundamental to verifying that a solution indeed meets the equation's requirements.

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