Simplify: \( 8w = 48 \)
How to Simplify the Equation \( 8w = 48 \): A Step-by-Step Guide
Solving equations is a fundamental skill in algebra, and simplifying expressions like \( 8w = 48 \) is essential for building strong problem-solving abilities. In this article, we’ll walk through the process of simplifying and solving the equation \( 8w = 48 \) in a clear, step-by-step manner—perfect for students, educators, and anyone looking to strengthen their math foundation.
What is the Equation \( 8w = 48 \)?
The equation \( 8w = 48 \) is a linear equation where \( w \) is a variable representing an unknown value. Our goal is to isolate \( w \) and determine its value.
Step 1: Understand the Equation
The expression \( 8w \) means “8 times \( w \)” — in other words, 8 multipled by the unknown variable \( w \). The equation states that this product equals 48.
To simplify and solve for \( w \), we reverse the multiplication by dividing both sides of the equation by 8.
Step 2: Solve for \( w \) by Dividing Both Sides
Start with the original equation:
\[8w = 48\]
Divide both sides by 8:
\[\frac{8w}{8} = \frac{48}{8}\]
Simplify both sides:
\[w = 6\]
Step 3: Verify the Solution
Plug \( w = 6 \) back into the original equation to check accuracy:
\[8w = 8 \ imes 6 = 48\]
Since both sides are equal, the solution is correct.
Why Simplifying \( 8w = 48 \) Matters
- Builds foundational algebra skills- Teaches how to isolate variables using inverse operations- Demonstrates the balance method in equation solving- Helps prepare for more complex equations involving variables
Summary
Simplifying \( 8w = 48 \) involves:
- Recognizing the equation form2. Dividing both sides by 83. Solving for \( w \) to get \( w = 6 \)4. Confirming the solution
Mastering this simple equation helps lay the groundwork for advanced math topics. Use these steps anytime you encounter a similar linear equation!
Bonus: Common Mistakes to Avoid
- Forgetting to divide both sides equally- Misapplying the division (e.g., only dividing 48)- Skipping the verification step
Always double-check your work!
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