["# Solve ( 2(3w + 3) = 54 ): Step-by-Step Guide and Explanation", "Understanding how to solve linear equations is essential in algebra, and one common type of problem students encounter is equations involving brackets, such as ( 2(3w + 3) = 54 ). This article guides you through solving this specific equation step-by-step, explains the mathematical logic, and highlights practical tips to build confidence in algebra.", "## What is the Equation ( 2(3w + 3) = 54 )?", "This equation represents a real-world or academic problem where a quantity involves multiplying a linear expression — ( 3w + 3 ) — by 2, resulting in 54. Solving it allows us to find the unknown variable ( w ), commonly referred to as a variable.", "## Step-by-Step Solution", "### Step 1: Simplify the Left Side
\nStart by distributing the 2 across the expression inside the parentheses:", "[
\n2(3w + 3) = 2 \cdot 3w + 2 \cdot 3 = 6w + 6
\n]", "So the equation becomes:", "[
\n6w + 6 = 54
\n]", "### Step 2: Isolate the Term with the Variable
\nSubtract 6 from both sides to move the constant term to the right-hand side:", "[
\n6w + 6 - 6 = 54 - 6
\n]", "[
\n6w = 48
\n]", "### Step 3: Solve for ( w )
\nDivide both sides by 6:", "[
\nw = \frac{48}{6} = 8
\n]", "## Final Answer", "The solution to the equation ( 2(3w + 3) = 54 ) is:", "[
\n\boxed{w = 8}
\n]", "## Why This Matters — Real-World Applications", "Linear equations like this one appear in budgeting, physics, engineering, and data analysis. For example, if ( w ) represents hours worked at $2 per hour plus a $6 fixed fee, the equation models total pay equaling $54. Solving helps confirm how many hours were worked.", "## Useful Tips for Solving Linear Equations", "- Distribute first when brackets contain an outer numeral (like 2 in this case).
\n- Isolate the variable term by undoing addition or subtraction on both sides.
\n- Divide evenly to find the variable’s value.
\n- Check your answer by substituting ( w = 8 ) back into the original equation:", "[
\n2(3 \cdot 8 + 3) = 2(24 + 3) = 2 \cdot 27 = 54 \quad \ ext{(Correct!)}
\n]", "## Summary", "Solving ( 2(3w + 3) = 54 ) follows basic algebra steps: distribute, simplify, isolate, and solve. Understanding this process builds a strong foundation for solving more complex equations. With practice, equations like this become clear and straightforward tools for problem-solving.", "---", "Keywords: solve linear equation, algebra 2(3w + 3) = 54, step-by-step algebra, solve for w, linear equations tutorial, intermediate algebra, equation solving tips", "Meta Description: Learn how to solve ( 2(3w + 3) = 54 ) step-by-step with clear explanations, practice tips, and real-world application. Perfect for students mastering basic algebra."]
