Solving the Equation: 2(3w + 5) = 58 – A Step-by-Step Guide

Mastering algebra is essential for students, educators, and anyone looking to strengthen problem-solving skills. One of the most common equation types involves distributing, combining terms, and isolating variables — and the equation 2(3w + 5) = 58 is a perfect example. In this SEO-friendly article, we’ll break down how to solve this equation clearly, accurately, and using keywords that boost visibility for learners seeking algebra help.

Understanding the Context

What is the Equation We’re Solving?

We begin with:
2(3w + 5) = 58

This equation tells us that twice the quantity (3w + 5) equals 58. To find the value of the variable w, we follow a standard sequence of operations: distributing, simplifying, isolating the variable, and solving.

1 58 Header Tubing | The Tube

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1 58 Header Tubing | The Tube
Given that: 5 = 5W+2ω / 5+2 and 5.1 = 7W+3ω / 7+3, find W and ω ...
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Solved ww-5-2w2w-5=w-12w2-15w+25 | Chegg.com
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Key Insights

Step-by-Step Solution

Step 1: Distribute the 2

Multiply 2 with both terms inside the parentheses:
2 × (3w + 5) = 2 × 3w + 2 × 5
→ 6w + 10 = 58

This step eliminates parentheses and prepares the equation for simplification.

Step 2: Subtract 10 from Both Sides

To isolate the term with the variable, subtract 10 from both sides:
6w + 10 – 10 = 58 – 10
→ 6w = 48

Step 3: Divide Both Sides by 6

Now divide both sides by 6 to solve for w:
6w ÷ 6 = 48 ÷ 6
→ w = 8

Continue Reading

Area using legs: \( \frac{1}{2} \times 9 \times 12 = 54 \) square cm.
Area using hypotenuse and altitude: \( \frac{1}{2} \times 15 \times h = 54 \).
So \( 15h = 108 \), \( h = 7.2 \) cm.

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Final Thoughts

Verification – Check the Solution

Plug w = 8 back into the original equation to confirm:
2(3(8) + 5) = 2(24 + 5) = 2 × 29 = 58 — matches perfectly!

Why This Equation Matters – Educational Relevance

Equations like 2(3w + 5) = 58 are foundational in algebra. They teach:

  • Distributive property: Multiplying across parentheses
  • Operations and balance: What you do to one side, do to the other
  • Solution strategies: Isolating variables through inverse operations

Parents and students often search for clear, step-by-step algebra solutions to reinforce classroom learning — and understanding such equations helps build confidence and analytical thinking.

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