Solving the Equation: 2(2w + 3 + w) = 54 → Simplifying to 2(3w + 3) = 54

Understanding and solving linear equations is a fundamental skill in algebra that forms the basis of more advanced mathematics. One common type of equation you often encounter is when parentheses are used with expressions involving variables. In this article, we’ll walk through step-by-step how to solve the equation:

2(2w + 3 + w) = 54,
and show how it simplifies neatly to:
2(3w + 3) = 54,
leading to an easy solution for w.

Understanding the Context

Step 1: Simplify the Expression Inside the Parentheses

The equation begins with:

2(2w + 3 + w) = 54

$\Rightarrow \quad \frac{a}{b}=\frac{3+1+2 \sqrt{3}}{3+1-2 \sqrt{3}} \Righ..$

Image Gallery

$\Rightarrow \quad \frac{a}{b}=\frac{3+1+2 \sqrt{3}}{3+1-2 \sqrt{3}} \Righ..$

Bright Quad LED 54 3W LED PAR Stage - 3W LED PAR and LED 54 3W PAR Light

Solved Find the product. (2w - 3)(3w+5) 2 (2w-3)(3w+5) = 6 + | Chegg.com

Key Insights

Before solving, combine like terms inside the parentheses:

2w + w = 3w
- The constant +3 remains.

So,
2w + 3 + w = 3w + 3

Now the equation becomes:
2(3w + 3) = 54

This matches the simplified form 2(3w + 3) = 54, as shown.

🔗 Related Articles You Might Like:

📰 Good Phone Plans 📰 Best Automatic Pool Cleaner 📰 Peacock Discounts 📰 Vzw Coverage Locator 1865128 📰 Urn Stock Is Explodingheres Why Every Trader Should Act Now Before It Crashes 1145487 📰 Master Java Synchronization Fastclick Here To Unlock Flawless Code Execution 3943080 📰 The Magic Number 75 Cm Inches Youve Been Ignoringdont Miss This 6271260 📰 Hydtrack The Secret Tool Tech Gurus Swear By For Smarter Water Management 6521747 📰 Mortise Secrets Every Diyer Must Know Before Starting Their Next Project 4707681 📰 From Wisdom To Wounds The Powerful Maya Angelou Quotes Everyone Needs To Hear 2315543 📰 The Number Of Years That Passed Between Newtons Introduction And Leibnizs Publication Is 19 6559050 📰 New Hipaa Tech Rules The Critical Requirements You Cant Afford To Ignore In 2024 2083925 📰 Why Xpo Stock Is The Hottest Dark Horse In The Marketdont Miss Out 6188089 📰 Secrets Revealed About Billy Billy Mandyno One Was Ready For This 8560753 📰 White Contacts That Make Your Eyes Sparkle Heres What You Need To Know Now 9978985 📰 When Did Vine Come Out 6733753 📰 Final Hours Of Jc Penney Inside The Massive Retail Store Shutdowns 8420175 📰 Deer Cartoon 641343

Final Thoughts

Step 2: Solve for w

Now, solve the simplified equation:

2(3w + 3) = 54

Divide both sides by 2
To isolate the parenthetical expression, divide both sides by 2:

$$
\frac{2(3w + 3)}{2} = \frac{54}{2}
\Rightarrow 3w + 3 = 27
$$

Subtract 3 from both sides

$$
3w + 3 - 3 = 27 - 3
\Rightarrow 3w = 24
$$

Divide both sides by 3

$$
w = \frac{24}{3} = 8
$$