Question

Is 2 a solution of $2 x^{2}-1=4 x-1 ?$

   Is 2 a solution of $2 x^{2}-1=4 x-1 ?$

Prealgebra and Introductory Algebra

Prealgebra and Introductory Algebra

Richard N. Aufmann,… 3rd Edition

Chapter 5, Problem 17

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Solved by Expert Ethan Somes

06/20/2020

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Step 1: We are given the equation $2 x^{2}-1=4 x-1$ and we want to check if $x=2$ is a solution. Show more…

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Is 2 a solution of $2 x^{2}-1=4 x-1 ?$

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Key Concepts

Algebraic Equation

An algebraic equation is a mathematical statement that shows the equality between two expressions involving one or more unknowns. Solving the equation means finding all values of the unknowns that can be substituted to make the equation true.

Quadratic Equation

A quadratic equation is a type of algebraic equation where the highest power of the variable is 2. It typically has the form ax² + bx + c = 0 and can have up to two solutions, which can be found by various methods such as factoring, completing the square, or using the quadratic formula.

Substitution Method

The substitution method involves replacing the variable in the equation with a specific value to determine if the equality holds. This technique is a straightforward way to verify if a particular number is a solution to the equation.

Solution Verification

Solution verification is the process of confirming that a potential solution satisfies the original equation. This involves substituting the value into the equation and checking whether both sides of the equation remain equal.

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