\( 2(2w + 3) = 34 \)

["How to Solve ( 2(2w + 3) = 34 ): Step-by-Step Guide", "Solving algebraic equations is a fundamental skill in mathematics, and one of the most common beginner-friendly problems is linear equations like ( 2(2w + 3) = 34 ). This equation is not only straightforward but also highly applicable in real-world scenarios. In this article, we’ll walk through how to solve ( 2(2w + 3) = 34 ) step-by-step, explaining each move clearly to strengthen your understanding.", "---", "### What Is the Equation ( 2(2w + 3) = 34 ) About?", "The equation ( 2(2w + 3) = 34 ) represents a simple linear relationship. It involves multiplying a binomial expression ( (2w + 3) ) by 2, and we want to find the value of the variable ( w ) that makes both sides equal.", "This type of equation appears frequently in algebra, helping students build problem-solving habits for more complex equations later.", "---", "### Step-by-Step Solution", "Step 1: Expand the Left Side", "Start by distributing the 2 across the parentheses:", "[\n2(2w + 3) = 2 \cdot 2w + 2 \cdot 3 = 4w + 6\n]", "So the equation becomes:", "[\n4w + 6 = 34\n]", "Step 2: Isolate the Term with ( w )", "Subtract 6 from both sides to eliminate the constant:", "[\n4w + 6 - 6 = 34 - 6\n]", "[\n4w = 28\n]", "Step 3: Solve for ( w )", "Divide both sides by 4:", "[\nw = \frac{28}{4} = 7\n]", "---", "### Final Answer", "[\n\boxed{w = 7}\n]", "---", "### Why Is This Equation Useful?", "- Real-world applications: Linear equations like this model situations such as calculating costs, distances, or temperatures.\n- Foundation for advanced math: Understanding how to isolate variables is key to solving systems of equations, quadratic equations, and beyond.\n- Problem-solving confidence: Mastering this equation builds mathematical intuition and logical thinking.", "---", "### How to Check the Solution", "Always verify your answer by plugging ( w = 7 ) back into the original equation:", "[\n2(2 \cdot 7 + 3) = 2(14 + 3) = 2 \cdot 17 = 34\n]", "Since both sides equal 34, the solution is correct.", "---", "### Summary", "Solving ( 2(2w + 3) = 34 ) involves distributing, simplifying, and isolating the variable—which follows clear, universal algebraic principles. Practice this problem regularly to build fluency, then apply these skills to more complex equations.", "---", "Keywords: equation solving, linear equations, algebra tutorial, solve (2(2w+3)=34), step-by-step math, how to solve (2(2w+3)=34), math problem steps, real-world math applications.", "---", "Combining clear explanation with practical verification, this guide helps students learn, review, and confidently apply solving equations like ( 2(2w + 3) = 34 ) in their math journey."]