How to Solve the Linear Equation: A Step-by-Step Guide to Solving 2(w + w + 4) = 40

When tackling algebra problems, especially linear equations, breaking them down step-by-step makes the process clearer and easier to follow. One common type of equation students encounter involves expressions with parentheses and combining like terms. In this article, we’ll walk through a classic example: solving 2(w + w + 4) = 40, demonstrating a systematic approach to solve for the variable w.

Understanding the Context

The Equation:

2(w + w + 4) = 40

Step 1: Simplify the expression inside the parentheses

Begin by combining like terms within the parentheses:
w + w + 4 = 2w + 4

So the equation becomes:
2(2w + 4) = 40

Perimeter: 2(w + w + 4) = 40 → 2(2w + 4) = 40 → 4w + 8 = 40 → 4w = 32 → w = 8

Key Insights

Step 2: Apply the distributive property

To eliminate the parentheses, multiply 2 by each term inside:
2 × 2w = 4w
2 × 4 = 8

Now the equation is:
4w + 8 = 40

Step 3: Isolate the variable term

Subtract 8 from both sides to isolate the term with w:
4w + 8 − 8 = 40 − 8
4w = 32

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Final Thoughts

Step 4: Solve for w

Divide both sides by 4 to solve for w:
4w ÷ 4 = 32 ÷ 4
w = 8

Final Answer:

✅ The solution to the equation 2(w + w + 4) = 40 is w = 8.

Why This Method Works

Understanding each step—simplifying expressions, applying the distributive property, isolating variables, and “undoing” operations—is fundamental to solving algebraic equations. These techniques help build logical reasoning skills essential not just in math, but in science, engineering, and everyday problem-solving.

Need More Practice?

Mastering linear equations like this one opens the door to more complex algebra topics. Whether you're studying for exams or learning basic math fundamentals, practicing step-by-step solutions ensures confidence and clarity.

Keywords: linear equations, algebraic equations, solving for w, step-by-step algebra, 2(w + w + 4) = 40, equation solving tutorial

Meta Description: Learn how to solve 2(w + w + 4) = 40 using step-by-step algebra. Simplify, distribute, isolate, and solve—step by step. Perfect for students mastering basic math equations.