6w + 6 = 54 \quad \Rightarrow \quad 6w = 48 \quad \Rightarrow \quad w = 8
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?
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 SidesTo isolate the term with w, start by removing the constant term on the left side. Subtract 6 from both sides:
\[6w + 6 - 6 = 54 - 6\]
Simplifying both sides gives:
\[6w = 48\]
Step 2: Divide Both Sides by 6Now that 6w = 48, divide both sides by 6 to solve for w:
\[\frac{6w}{6} = \frac{48}{6}\]
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 MattersUnderstanding 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.
Related Search Terms:- How to solve 6w + 6 = 54- Step-by-step linear equation solving- Algebra basics for students- Solving equations with addition and multiplication
By following these clear steps, breaking down equations becomes easier—empowering your journey in math and beyond!
