Determine whether each value of x is a solution of the equation. Equation Values (

step 1 All right. So we're giving under word problem on solving equations and inequalities and here we'

Determine whether each value of x is a solution of the...

Determine whether each value of $x$ is a solution of the equation.
$$\begin{array}{cc}\text{Equation} && \text{Values} \\ \frac{5}{2 x}-\frac{4}{x}=3&&a. x=-\frac{1}{2} \quad b. x=4 \quad c. x=0 \quad d. x=\frac{1}{4} \end{array}$$

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Key Concepts

Substitution for Verification

Substitution is the process of replacing the variable with candidate numbers to test if the original equation holds true. This method is particularly useful in verifying whether a proposed solution actually satisfies the equation or if it was inadvertently introduced during the solving process.

Rational Equations

A rational equation is one that includes one or more expressions that are ratios of polynomials. Solving such equations often requires finding a common denominator or multiplying through by the least common denominator to eliminate fractions, while being careful about any restrictions on the variable.

Domain Restrictions

In equations involving fractions, it is crucial to identify values that make any denominator zero, as these are not part of the domain of the function. This step prevents considering invalid or extraneous solution candidates that would lead to undefined expressions.

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