In Exercises 1–26, solve and check each linear equation. 3(x - 1) = 21

Key Concepts

Linear Equations

A linear equation is an algebraic expression that represents a straight line when graphed. It typically takes the form ax + b = c, where a, b, and c are constants, and x is the variable. Solving a linear equation involves isolating the variable to find its value, which satisfies the equation.

Distributive Property

The distributive property is a fundamental algebraic principle that states a(b + c) = ab + ac. In the context of solving equations, it allows us to eliminate parentheses by multiplying a term outside the parentheses by each term inside. This property is essential for simplifying expressions and solving equations efficiently.

Checking Solutions

Checking solutions involves substituting the found value of the variable back into the original equation to verify its correctness. This step ensures that the solution satisfies the equation, confirming that no errors were made during the solving process. It is a crucial practice in algebra to validate the accuracy of the solution.