Solve the Equation 2(w + 2w) = 72: Step-by-Step Guide

If you're tackling algebra, you’ve likely encountered expressions like 2(w + 2w) = 72. This equation is a common starting point for students learning to simplify expressions and solve linear equations. In this SEO-optimized article, we’ll explore how to solve 2(w + 2w) = 72 step-by-step, explain the logic behind each step, and offer tips to master similar problems.

Understanding the Context

What is the Equation 2(w + 2w) = 72 All About?

The equation 2(w + 2w) = 72 involves simplifying a linear expression inside parentheses and solving for the unknown variable w. It’s a great example of combining like terms and applying basic algebraic operations.

Why solve equations like this?
Solving linear equations strengthens foundational algebra skills, prepares students for more advanced math, and appears frequently on standardized tests and school assessments.

[ANSWERED] Multiply 2w w 3w 3 2w w 3w 3 Simplify your answer - Kunduz

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[ANSWERED] Multiply 2w w 3w 3 2w w 3w 3 Simplify your answer - Kunduz
Solved: Factorise 2w^2+w-3 [Math]
Solved ww-5-2w2w-5=w-12w2-15w+25 | Chegg.com
7-w+2>36-2w - Gauthmath
Solved 2w, ws - 1 2 8 (W) - 2w + 2w, -1 sws 1 2w9 + 2w?, w > | Chegg.com

Key Insights

Step-by-Step Solution

Step 1: Combine like terms inside the parentheses

Inside the parentheses, w + 2w:
- Both terms involve w, so add the coefficients:
\( 1w + 2w = 3w \)

Now rewrite the equation:
\[
2(3w) = 72
\]

Step 2: Multiply the constants

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But wait—this is quadratic, but the problem states $ p(x) $ is cubic. Contradiction? Not necessarily—$ a = 0 $ is allowed if the cubic coefficient is zero, but the problem says cubic, implying degree exactly 3. So we must assume it's cubic, but our solution gives $ a = 0 $. That means the data fits a quadratic, but we are told it's cubic. So either the model is misclassified, or we must accept the interpolating polynomial, regardless of degree. Since the interpolation yields a unique cubic (degree at most 3), and we found $ a = 0 $, the polynomial is actually quadratic. But the problem says cubic, so we must reconsider.
Wait—perhaps the problem allows degree ≤ 3. Many contest problems phrase cubic loosely. Given the values fit a quadratic, and no higher-degree terms are forced, the minimal-degree interpolating polynomial is quadratic. Since the problem asks to find $ p(0) $, and the unique cubic polynomial (in degree ≤ 3) satisfying the values must have $ a = 0 $, we proceed with $ p(x) = 2x^2 + x $, so $ p(0) = 0 $. However, to ensure degree 3, suppose we include a zero cubic term. Then $ p(x) = 0x^3 + 2x^2 + x + 0 $, and $ p(0) = 0 $.
But let's verify all values:

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Final Thoughts

Multiply 2 by 3w:
\[
6w = 72
\]

Step 3: Isolate the variable

Divide both sides by 6 to solve for w:
\[
w = \frac{72}{6} = 12
\]

✅ Final Answer

\[
\boxed{w = 12}
\]

How to Check the Answer

Pull w = 12 back into the original equation to verify:
\[
2(12 + 2 \cdot 12) = 2(12 + 24) = 2(36) = 72
\]
✔️ The equation holds true.