In Exercises 15–35, solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 7(x-4) = x + 2

Verified step by step guidance

1. Distribute the 7 on the left side: 7(x - 4) becomes 7x - 28.
2. Rewrite the equation: 7x - 28 = x + 2.
3. Subtract x from both sides to get all x terms on one side: 7x - x - 28 = 2.
4. Simplify the equation: 6x - 28 = 2.
5. Add 28 to both sides to isolate the term with x: 6x = 30.

Key Concepts

Solving Linear Equations

Solving linear equations involves finding the value of the variable that makes the equation true. This typically requires isolating the variable on one side of the equation through operations such as addition, subtraction, multiplication, and division. In the given equation, 7(x-4) = x + 2, you would first distribute and then combine like terms to solve for x.

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 determining the nature of the solution after solving the equation.

Combining Like Terms

Combining like terms is a fundamental algebraic technique used to simplify expressions and equations. It involves adding or subtracting terms that have the same variable raised to the same power. In the context of the equation 7(x-4) = x + 2, this step is crucial after distributing to simplify both sides before isolating the variable.