Understanding the Equation 6w + 6 = 54: Step-by-Step Breakdown

Solving equations is a fundamental skill in mathematics that helps build logical reasoning and problem-solving abilities. One common type of equation encountered is linear equations like 6w + 6 = 54. If you’ve come across this equation and wondered how to solve it step-by-step, you’re in the right place.

What Does the Equation Mean?

Understanding the Context

The equation 6w + 6 = 54 states that six times a number w, increased by six, equals fifty-four. Solving this means finding the value of w that makes the equation true.

Step 1: Subtract 6 from Both Sides
To isolate the term with w, start by removing the constant term on the left side. Subtract 6 from both sides:

\[
6w + 6 - 6 = 54 - 6
\]

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\Rightarrow \quad \frac{n !}{(n-1) !}=9 \quad \Rightarrow \quad \frac{n(n..

Key Insights

Simplifying both sides gives:

\[
6w = 48
\]

Step 2: Divide Both Sides by 6
Now that 6w = 48, divide both sides by 6 to solve for w:

\[
\frac{6w}{6} = \frac{48}{6}
\]

Continue Reading

Recognize the expression as a difference of squares:
x^4 - 16y^4 = (x^2)^2 - (4y^2)^2 = (x^2 - 4y^2)(x^2 + 4y^2)
Now, note that \(x^2 - 4y^2\) is also a difference of squares:

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Final Thoughts

This simplifies to:

\[
w = 8
\]

Final Answer:
\[
\boxed{w = 8}
\]

Verification:
Plug w = 8 back into the original equation:
\[
6(8) + 6 = 48 + 6 = 54
\]
The left-hand side equals the right-hand side, confirming the solution is correct.

Why This Equation Matters
Understanding how to solve equations like 6w + 6 = 54 prepares you for more complex math topics, including algebra, calculus, and real-world applications in science, engineering, and finance. Practicing basic algebra builds confidence and a strong foundation.

If you're learning algebra or helping someone study, breaking equations into clear, logical steps is key. Mastering these fundamentals leads to long-term success in mathematics.

Key Takeaways:
- Start by isolating terms with the variable.
- Use inverse operations to maintain equation balance.
- Always verify your solution by substituting back.
- Linear equations like this form the basis of algebra.