Solving the Equation 2(w + 3w) = 64: A Step-by-Step Guide with Common Problems Explained

Understanding and Solving the Equation 2(w + 3w) = 64

Understanding the Context

Equations are fundamental tools in algebra that help us find unknown values by balancing expressions. One common type is linear equations involving parentheses and combined like terms. An equation like 2(w + 3w) = 64 might seem simple, but mastering its solution builds a strong foundation for more complex math concepts.

If you're learning algebra or reviewing linear equations, solving something like 2(w + 3w) = 64 helps develop essential problem-solving skills. In this article, we’ll break down the steps to solve this equation, explain why each step matters, and clarify any common pitfalls students encounter.

Step 1: Simplify the Expression Inside the Parentheses

Key Insights

Start by combining like terms inside the parentheses:
w + 3w = 4w

So the equation becomes:
2(4w) = 64

This simplification is crucial—it reduces complexity and reveals the equation’s true form: 8w = 64

Step 2: Isolate the Variable w

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Final Thoughts

To solve for w, divide both sides of the equation by 2:
(8w)/2 = 64/2
4w = 64

Dividing by the coefficient of w isolates the variable, making it easier to find its value. (Always divide both sides by the same number to maintain equation balance.)

Step 3: Solve for w by Dividing Both Sides by 4

Now divide both sides by 4:
4w ÷ 4 = 64 ÷ 4
w = 16

This final step gives you the value of w. Always check your solution by substituting w = 16 back into the original equation.

Step 4: Verification — Plug the Solution Back In

Substitute w = 16 into 2(w + 3w) = 64:
Left side:
2(16 + 3×16) = 2(16 + 48) = 2(64) = 128
Wait — that’s not equal to 64!

But hold on—let’s double-check the arithmetic carefully: