In Exercises 1–26, solve and check each linear equation. 4x + 9 = 33

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.

Isolating the Variable

Isolating the variable is a fundamental technique in solving linear equations. This process involves performing operations such as addition, subtraction, multiplication, or division to get the variable alone on one side of the equation. For example, in the equation 4x + 9 = 33, you would first subtract 9 from both sides to simplify the equation.

Checking Solutions

Checking solutions is the process of 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. For instance, if x = 6 is found, substituting it back into 4x + 9 should yield 33.