\[ 5h + 3(2h - 4) = 15 \]

["Solving the Linear Equation: 5h + 3(2h - 4) = 15 – A Step-by-Step Guide", "Plumbing a linear equation in algebra can feel like decoding a puzzle — especially when parentheses and coefficients are involved. One commonly encountered equation is:", "[ 5h + 3(2h - 4) = 15 ]", "Whether you’re a student learning algebra or a teacher guiding learners, understanding how to solve this equation step-by-step is essential. In this article, we’ll break down the solution clearly and explore how to use it in real-world math contexts.", "---", "### Understanding the Equation", "The equation\n[ 5h + 3(2h - 4) = 15 ]\nis a linear expression involving one variable, ( h ). Our goal is to isolate ( h ) and find its value.", "---", "### Step 1: Expand the Parentheses", "The first crucial step is to eliminate the parentheses by applying the distributive property:", "[ 3(2h - 4) = 3 \cdot 2h - 3 \cdot 4 = 6h - 12 ]", "Now rewrite the equation:\n[ 5h + 6h - 12 = 15 ]", "---", "### Step 2: Combine Like Terms", "Combine the terms containing ( h ):\n[ (5h + 6h) - 12 = 15 ]\n[ 11h - 12 = 15 ]", "---", "### Step 3: Isolate the Variable Term", "Add 12 to both sides to move the constant to the right:\n[ 11h = 15 + 12 ]\n[ 11h = 27 ]", "---", "### Step 4: Solve for ( h )", "Now divide both sides by 11:\n[ h = \frac{27}{11} ]", "This is the solution in its simplest fractional form. You can convert it to a decimal:\n[ h \approx 2.45 ]", "---", "### Why This Equation Matters", "Solving linear equations like ( 5h + 3(2h - 4) = 15 ) develops critical algebraic skills. These skills apply in fields such as physics, economics, and computer science, where relationships between variables often follow linear models.", "---", "### Final Answer", "The solution to the equation\n[ 5h + 3(2h - 4) = 15 ]\nis\n[ h = \frac{27}{11} ]", "---", "### Want to Master More Algebra?", "- Review distributive property and combining like terms\n- Practice solving equations step-by-step\n- Explore real-world word problems involving linear models", "With consistent practice, equations like this become manageable—and even enjoyable!", "---", "Keywords: solve 5h + 3(2h - 4) = 15, algebra tutorial, linear equations, solve for h, school math, step-by-step solving, equation expansion, distributive law, algebra practice"]