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

Verified step by step guidance

1. Distribute the 4 on the left side of the equation: \(4(x + 9) = 4x + 36\).
2. Set the equation equal to the right side: \(4x + 36 = x\).
3. Subtract \(x\) from both sides to get all terms involving \(x\) on one side: \(4x - x + 36 = 0\).
4. Simplify the equation: \(3x + 36 = 0\).
5. Subtract 36 from both sides to isolate the term with \(x\): \(3x = -36\).

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 on one side of the equation to find its value.

Distributive Property

The distributive property states that a(b + c) = ab + ac. This property is essential for simplifying expressions where a term is multiplied by a sum or difference. In the context of the given equation, applying the distributive property allows us to eliminate parentheses and combine like terms effectively.

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 part of solving linear equations to ensure accuracy.