In Exercises 15–35, solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 2x-5 = 7

Key Concepts

Solving Linear Equations

Solving linear equations involves finding the value of the variable that makes the equation true. In the equation 2x - 5 = 7, we isolate x by performing inverse operations, such as adding 5 to both sides and then dividing by 2. This process is fundamental in algebra as it allows us to determine specific values that satisfy the equation.

Types of Equations

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 analyzing the nature of the solutions obtained from solving an equation.

Verification of Solutions

After solving an equation, it is essential to verify the solution by substituting it back into the original equation. This step confirms whether the derived value satisfies the equation. For example, substituting the solution of 2x - 5 = 7 back into the equation allows us to check if both sides are equal, thus validating the solution and determining the type of equation.