6w + 6 = 54 \quad \Rightarrow \quad 6w = 48 \quad \Rightarrow \quad w = 8 - Decision Point
Understanding the Equation 6w + 6 = 54: Step-by-Step Breakdown
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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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:
\[
\frac{6w}{6} = \frac{48}{6}
\]
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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.
