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

🔗 Related Articles You Might Like:

📰 This 3D Pen Will Change How You Create Art—Shock Users with Incredible 3D Prints! 📰 Unlock Limitless Creativity: How the 3D Pen Is Revolutionizing 3D Printing! 📰 3D Pen Magic: Want to Print in 3D Without a Printer? Try This Game-Changer! 📰 Last Chance Movies Out Soon Stream These Before They Disappear Forever 📰 Last Chance To Explore The Alluring Milfs Of Japan Exclusive Reveal 📰 Last Chance To Play Minecraft On Xbox 360 Heres The Ultimate Guide You Need Before Its Gone 📰 Last Minute Update On 2024S Hottest Movies Dont Miss These Blockbuster Releases 📰 Last Seen In Season 1Moon Knights Return In Season 2 Kills This Character Drama 📰 Last Stand By Mr Monk The Epic Monk Movie That Everyones Talking About 📰 Latest Blockbusters Are Streaming Now Watch The Top Titles Instantly 📰 Latest Movies New To Streamingworth Bingeing Guaranteed 📰 Le Cot Des Bananes Est De 15 030 450 📰 Le Cot Des Oranges Est De 8 070 560 📰 Le Cot Des Pommes Est De 10 050 5 📰 Le Cot Total Est De 5 450 560 1510 📰 Le Nouveau Volume Est De 5 Litres X Litres 📰 Le Point Milieu Le Centre Et Un Extrme De La Corde Forment Un Triangle Rectangle 📰 Le Primtre Est Donn Par 2W 2W 36 Cm Ce Qui Se Simplifie En 6W 36 Cm

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: