Question

Solve and check. $$x-\frac{1}{2}=\frac{1}{2}$$

   Solve and check.
$$x-\frac{1}{2}=\frac{1}{2}$$

Prealgebra and Introductory Algebra

Prealgebra and Introductory Algebra

Richard N. Aufmann,… 3rd Edition

Chapter 5, Problem 51

Instant Answer

Solved by Expert Ethan Somes

06/21/2020

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Solve and check. $$x-\frac{1}{2}=\frac{1}{2}$$

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Key Concepts

Solution Verification

Solution verification is the process of substituting the determined value back into the original equation to confirm that both sides of the equation are equivalent. This final check ensures that the solution is correct and that no mistakes were made during the algebraic manipulations.

Isolating the Variable

Isolating the variable is a fundamental strategy in solving equations, where operations are applied to both sides of the equation to leave the unknown variable by itself. This step-by-step process involves undoing any operations affecting the variable, enabling a straightforward computation of its value.

Linear Equations

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a variable raised to the first power. Such equations form a straight line when graphed and are typically solved by isolating the variable on one side to determine its value.

Inverse Operations

Inverse operations are methods used to reverse or cancel out the operations applied to the variable. For example, if a number is added to the variable, subtracting the same number from both sides undoes that addition; similarly, multiplying and dividing are inverse operations. These techniques are essential for systematically reducing the equation to a form where the variable can be directly solved.

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