Simplify and solve for \( w \): \( 4w + 10 + 2w = 54 \) becomes \( 6w + 10 = 54 \).
["How to Simplify and Solve the Equation ( 4w + 10 + 2w = 54 ): Step-by-Step Guide", "Working with linear equations is a fundamental skill in algebra, and simplifying them step by step makes solving easier and more intuitive. One common challenge students face is correctly combining like terms before isolating the variable. This article explains how to simplify the equation ( 4w + 10 + 2w = 54 ) into ( 6w + 10 = 54 ), and solves for ( w ) clearly and confidently.", "---", "### Step 1: Combine Like Terms on the Left Side", "Start with the original equation:\n[\n4w + 10 + 2w = 54\n]", "Identify the terms with the variable ( w ):\n- ( 4w ) and ( 2w ) are like terms.", "Add them together:\n[\n(4w + 2w) + 10 = 54\n]\n[\n6w + 10 = 54\n]", "This simplification step reduces the equation’s complexity and focuses only the key variable terms.", "---", "### Step 2: Eliminate Constants to Isolate the Variable", "Now the simplified equation is:\n[\n6w + 10 = 54\n]", "To isolate ( 6w ), subtract 10 from both sides:\n[\n6w + 10 - 10 = 54 - 10\n]\n[\n6w = 44\n]", "This step removes the constant term introduced in the original equation and prepares you to solve for ( w ).", "---", "### Step 3: Solve for ( w ) by Dividing Both Sides", "To isolate ( w ), divide both sides of ( 6w = 44 ) by 6:\n[\nw = \frac{44}{6}\n]", "Simplify the fraction:\n[\nw = \frac{22}{3} \quad \ ext{or} \quad w \approx 7.33\n]", "---", "### Final Answer", "The solution to the equation ( 4w + 10 + 2w = 54 ) is:\n[\nw = \frac{22}{3}\n]", "---", "### Why This Works: Key Takeaways", "- Combine like terms to simplify expressions and focus on what matters.\n- Always isolate the variable by removing constants before dividing.\n- Simplifying equations step-by-step makes solving more manageable and reduces errors.", "Mastering each of these steps builds strong algebraic reasoning—essential for more advanced math. Practice these skills, and solving linear equations will become second nature!", "---", "Keywords for SEO:\nLinear equations, solve for ( w ), simplify ( 4w + 10 + 2w = 54 ), algebraic steps, solving linear equations, step-by-step algebra, math tutorial, equation simplification, fraction solution."]
