2(w + 3w) = 64 - All Square Golf
Solving the Equation 2(w + 3w) = 64: A Step-by-Step Guide with Common Problems Explained
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
Image Gallery
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:
📰 \[ f'(u) = 5u^4 - 9u^2 + 2 \] 📰 \[ f'(1) = 5(1)^4 - 9(1)^2 + 2 = 5 - 9 + 2 = -2 \] 📰 \[ a = -2 \] 📰 Longest Serving Pope 7361610 📰 You Wont Believe How This Cutting Tool Cuts Rope Like A Pro In Just 2 Seconds 2895288 📰 4 Discover The Ultimate Collection Of Best Nintendo Ds Games You Need To Relive 6794600 📰 Cast Of The Way We Were Movie 1600090 📰 Best Game 7 In World Series History Sudden Shocking Twists Inside 8347172 📰 Celebrity News Celebrity News 742997 📰 Unlock Excel Secrets Hack That Boosts Productivity Overnight 220677 📰 Hellboys Forbidden Trade The Golden Army That Powers The Darkest Warriors 9700008 📰 Life Mart Reviews Is This The Secret To Smarter Faster Shopping 4180461 📰 Which Android Device Works Best With Wsa 6011543 📰 Java Se Development Kit For Mac The Secret Tool Making Coding Easier Than Ever 3154782 📰 Dr Patels Forbidden Prescription That Doctors Fear To Reveal 2681905 📰 Big News The 725 New Balance Shocked Everyone With These Unbeatable Prices 4574188 📰 Erin Brodie 4063531 📰 Foreclosed Property Near Me 7191530Final 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:
