Solve: \( \frac{3d + 2d}{180} = 5 \) gives \( 5d = 900 \), so \( d = 180 \) km.
["How to Solve the Equation ( \frac{3d + 2d}{180} = 5 ) – A Step-by-Step Guide", "Solving linear equations like ( \frac{3d + 2d}{180} = 5 ) is a fundamental skill in algebra that helps simplify real-life math problems involving distances, rates, and proportions. In this article, we’ll walk through how to solve this equation step-by-step and explain how it leads to the solution ( d = 180 ) km.", "---", "### Understanding the Equation", "We begin with:\n[\n\frac{3d + 2d}{180} = 5\n]", "This equation represents a situation where the combined distance (modeled by ( 3d + 2d )) over 180 km is equal to 5 units—likely a rate or ratio given in the problem context.", "---", "### Step 1: Combine Like Terms", "Combine the terms in the numerator:", "[\n3d + 2d = 5d\n]", "So the equation simplifies to:", "[\n\frac{5d}{180} = 5\n]", "---", "### Step 2: Eliminate the Denominator", "Multiply both sides by 180 to isolate the numerator:", "[\n5d = 5 \ imes 180\n]", "[\n5d = 900\n]", "---", "### Step 3: Solve for ( d )", "Now divide both sides by 5:", "[\nd = \frac{900}{5} = 180\n]", "Thus, ( d = 180 ) km.", "---", "### What Does ( d = 180 ) Mean in a Real Context?", "In problems involving travel, speed, or distance, ( d ) often represents an unknown distance. Here, ( d = 180 ) km means the distance covered (scaled by the equation) corresponds to a scenario yielding a total result of 5 units when combined and averaged over 180 km — a proportional relationship consistent with speed and time.", "---", "### Summary", "Solving ( \frac{3d + 2d}{180} = 5 ) yields:", "- Combine terms: ( 5d )\n- Eliminate denominator: ( 5d = 900 )\n- Solve: ( d = 180 )", "This method highlights key algebraic techniques: simplifying expressions, eliminating fractions, and isolating variables — essential skills for tackling similar equations in physics, engineering, or everyday math.", "---", "If you're studying algebra or preparing for more complex equations, mastering such steps builds confidence and clarity. This simple yet powerful approach forms the foundation for solving equations involving proportions, rates, and real-world applications.", "---", "Key Takeaway: Solving equations step-by-step—combining terms, eliminating denominators, isolating variables—leads directly to the solution ( d = 180 ) km.", "---", "Keywords: solve linear equation, algebra steps, solve ( \frac{3d + 2d}{180} = 5 ), step-by-step equation solving, real-world math applications, ( d = 180 ) km"]
