In Exercises 1–26, solve and check each linear equation. 3(x - 8) = x

Verified step by step guidance

1. Distribute the 3 on the left side: \(3(x - 8) = 3x - 24\).
2. Set the equation equal to the right side: \(3x - 24 = x\).
3. Subtract \(x\) from both sides to get all \(x\) terms on one side: \(3x - x - 24 = 0\).
4. Simplify the equation: \(2x - 24 = 0\).
5. Add 24 to both sides to isolate the \(x\) term: \(2x = 24\).

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. This property allows us to multiply a single term by each term within a set of parentheses. In the context of the given equation, applying the distributive property helps simplify expressions before solving for the variable.

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.