The equations in Exercises 79–90 combine the types of equations we have discussed in this section. Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation.2/x + 1/2 = 3/4

In algebra, equations can be classified into three main types: identities, conditional equations, and inconsistent equations. An identity is true for all values of the variable, a conditional equation is true for specific values, and an inconsistent equation has no solutions. Understanding these classifications helps in determining the nature of the solution set for any given equation.

Rational equations involve fractions with variables in the denominator. To solve these equations, one typically finds a common denominator to eliminate the fractions, allowing for easier manipulation and simplification. This process is crucial for isolating the variable and determining the solution accurately.

After solving an equation, it is essential to check the solution by substituting it back into the original equation. This verification process ensures that the solution is valid and helps identify the type of equation. It confirms whether the equation holds true for the found value, thus determining if it is an identity, conditional, or inconsistent.