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

Verified step by step guidance

1. Start by applying the distributive property to the left side of the equation: multiply 4 by both x and 9 to get \(4 \times x + 4 \times 9\).
2. Rewrite the equation after distribution as \(4x + 36 = x\).
3. Next, get all the variable terms on one side by subtracting \(x\) from both sides: \(4x - x + 36 = 0\).
4. Simplify the variable terms to combine like terms: \(3x + 36 = 0\).
5. Isolate \(x\) by subtracting 36 from both sides and then dividing both sides by 3: \(3x = -36\) then \(x = \frac{-36}{3}\).

Key Concepts

Distributive Property

The distributive property allows you to multiply a single term by each term inside parentheses. For example, in 4(x + 9), you multiply 4 by x and 4 by 9, resulting in 4x + 36. This step simplifies the equation and prepares it for solving.

Solving Linear Equations

Solving linear equations involves isolating the variable on one side of the equation using inverse operations like addition, subtraction, multiplication, or division. The goal is to find the value of the variable that makes the equation true.

Checking Solutions

After finding a solution, substitute it back into the original equation to verify its correctness. This step ensures that the solution satisfies the equation and helps identify any errors made during solving.