Substitute into (1): $ 2(70 - 4d) + 3d = 60 $ → $ 140 - 8d + 3d = 60 $ → $ -5d = -80 $ → $ d = 16 $

["Understanding How to Solve the Equation $ 2(70 - 4d) + 3d = 60 $ – Step-by-Step Explanation", "Solving algebraic equations is a fundamental skill in mathematics, empowering students and problem solvers alike to uncover unknown values efficiently. One common equation students encounter is:", "$$\n2(70 - 4d) + 3d = 60\n$$", "This equation combines parentheses, distribution, and combining like terms, making it a great example to walk through step-by-step. In this article, we’ll explore how to solve it correctly and clearly — including why $ d = 16 $ is the accurate solution.", "---", "### Step 1: Expand the Parentheses", "Start by distributing the 2 across the expression inside the parentheses:", "$$\n2(70 - 4d) = 2 \ imes 70 - 2 \ imes 4d = 140 - 8d\n$$", "Now substitute back into the original equation:", "$$\n140 - 8d + 3d = 60\n$$", "---", "### Step 2: Combine Like Terms", "Next, combine the $ d $-terms on the left-hand side:", "$$\n-8d + 3d = -5d\n$$", "So the equation becomes:", "$$\n140 - 5d = 60\n$$", "---", "### Step 3: Isolate the Variable Term", "To solve for $ d $, subtract 140 from both sides:", "$$\n140 - 5d - 140 = 60 - 140\n$$", "$$\n-5d = -80\n$$", "---", "### Step 4: Solve for $ d $", "Divide both sides by $ -5 $:", "$$\nd = \frac{-80}{-5} = 16\n$$", "---", "### Final Answer", "$$\nd = 16\n$$", "---", "### Why This Matters (and How to Remember Each Step)", "Understanding each step helps reduce algebraic errors and builds confidence in solving more complex equations. Here’s a quick recall mental checklist:", "- Distribute thoroughly before combining terms\n- Watch signs carefully—especially when subtracting 140\n- Verify by plugging $ d = 16 $ back into the original equation:", "$$\n2(70 - 4(16)) + 3(16) = 2(70 - 64) + 48 = 2(6) + 48 = 12 + 48 = 60\n$$", "✅ Confirmed — $ d = 16 $ is correct.", "---", "### Practice Tips", "To master equations like this, practice similar expressions daily:", "Try solving:\n$ 5(30 - d) + 2d = 95 $\nor\n$ 3(50 + 2d) - 4d = 78 $", "Use the same step-by-step approach — expand, combine terms, isolate, solve.", "---", "In summary, solving $ 2(70 - 4d) + 3d = 60 $ reveals a clean, linear solution when each algebraic rule is applied carefully. The value $ d = 16 $ consistently emerges, proving the power of systematic problem-solving in algebra. Start practicing today — your math skills will grow stronger with every equation.", "---", "Keywords: solve linear equation, algebra techniques, step-by-step solving, $ 2(70 - 4d) + 3d = 60 $, equation solving, math problem solving, algebra practice, substitution and simplification, $ d = 16 $, solving equations algebraically."]