-\frac{7}{6} + \frac{63}{6} - \frac{164}{6} + d = 3

["# Solving the Equation: (-\frac{7}{6} + \frac{63}{6} - \frac{164}{6} + d = 3) Explained", "Learning how to solve equations like (-\frac{7}{6} + \frac{63}{6} - \frac{164}{6} + d = 3) is a fundamental skill in algebra. This equation combines fractions with a variable and a constant, offering a clear example of working with rational numbers. In this article, we’ll break down each step of solving for ( d ), clarify common pitfalls, and explain why understanding fractions is essential in algebra.", "## Step-by-Step Solution", "Start by simplifying the left-hand side of the equation, where all terms are fractions with denominator 6:", "[\n-\frac{7}{6} + \frac{63}{6} - \frac{164}{6} = \frac{-7 + 63 - 164}{6} = \frac{-98}{6}\n]", "Now rewrite the full equation:", "[\n\frac{-98}{6} + d = 3\n]", "To isolate ( d ), subtract (\frac{-98}{6}) from both sides (or add its opposite, (+\frac{98}{6})):", "[\nd = 3 + \frac{98}{6}\n]", "Convert 3 to fractions with denominator 6:", "[\n3 = \frac{18}{6}\n]", "Now add:", "[\nd = \frac{18}{6} + \frac{98}{6} = \frac{116}{6}\n]", "Simplify the fraction:", "[\nd = \frac{58}{3}\n]", "---", "## Final Answer", "[\n\boxed{d = \frac{58}{3}}\n]", "---", "## Why Fractions Matter in Algebra", "Working with fractions is crucial when solving equations because real-world problems and theoretical expressions often involve rational numbers. Simplifying and combining fractions efficiently allows clearer manipulation and accurate solutions. In this example:", "- Combining fractions requires a common denominator.\n- Operations like addition and subtraction hinge on clear numerator calculations.\n- Proper simplification reduces errors and improves readability.", "---", "## Tips for Students", "- Always simplify coefficients to their lowest terms when possible.\n- Convert whole numbers to fractions to work with a common denominator.\n- Double-check arithmetic to avoid small mistakes in addition or division.\n- Practice with negative fractions—they appear frequently and challenge many beginners.", "---", "Understanding how to solve equations involving fractions like (-\frac{7}{6} + \frac{63}{6} - \frac{164}{6} + d = 3) builds a strong foundation in algebra. With consistent practice and attention to detail, mastering these skills becomes not only possible but rewarding.", "If you want more algebraic practice or step-by-step guides, explore resources on combining like terms, fraction arithmetic, and variable isolation!"]