-\frac{108}{6} + d = 3 \implies -18 + d = 3 \implies d = 21

["### Solving Linear Equations: A Step-by-Step Guide", "Understanding how to solve simple linear equations is a foundational skill in algebra. One common type of problem involves isolating a variable to find its value. In this article, we’ll explore how to solve the equation (-\frac{108}{6} + d = 3), walk through the solution step-by-step, and arrive at the correct value for (d). By mastering these steps, you’ll better understand how to manipulate equations and strengthen your problem-solving abilities.", "---", "### Step 1: Simplify the Fraction", "The equation starts as:", "[\n-\frac{108}{6} + d = 3\n]", "Begin by simplifying the fraction. Divide 108 by 6:\n[\n\frac{108}{6} = 18\n]", "Because the fraction is negative, we have:\n[\n-18 + d = 3\n]", "---", "### Step 2: Isolate the Variable (d)", "To solve for (d), we must isolate it on one side. Since (-18) is being added to (d), reverse the operation by adding 18 to both sides of the equation:", "[\n-18 + d + 18 = 3 + 18\n]", "This simplifies to:\n[\nd = 21\n]", "---", "### Step 3: Verify the Solution", "It’s always good practice to check your answer by substituting (d = 21) back into the original equation:\n[\n-\frac{108}{6} + 21 = -18 + 21 = 3\n]", "Since the left side equals the right side, the solution is correct.", "---", "### Why This Matters: Solving Linear Equations", "Working through equations like (-\frac{108}{6} + d = 3) builds essential algebraic skills. These include:", "- Simplifying fractions\n- Performing inverse operations\n- Isolating variables\n- Checking solutions", "Mastering these principles prepares you for more complex algebra topics such as systems of equations, quadratic equations, and functions.", "---", "### Final Result", "The solution to the equation\n[\n-\frac{108}{6} + d = 3\n]\nis:\n[\n\boxed{d = 21}\n]", "Understanding every step ensures accuracy and confidence when tackling future math problems. Keep practicing — algebra becomes easier with each equation solved!"]