-\frac{49}{6} + \frac{189}{6} + c = -4

["Solving the Equation: (-\frac{49}{6} + \frac{189}{6} + c = -4)", "In algebra, solving equations step by step helps clarify the solution and strengthens foundational math skills. One such equation students often encounter involves combining fractions before isolating the unknown variable. This article explains how to solve:", "[\n-\frac{49}{6} + \frac{189}{6} + c = -4\n]", "---", "### Step-by-Step Solution", "Step 1: Combine the constant fractions", "Since the denominators are the same, you can add the numerators directly:", "[\n-\frac{49}{6} + \frac{189}{6} = \frac{-49 + 189}{6} = \frac{140}{6}\n]", "Simplify (\frac{140}{6}):", "[\n\frac{140 \div 2}{6 \div 2} = \frac{70}{3}\n]", "Now the equation becomes:", "[\n\frac{70}{3} + c = -4\n]", "---", "Step 2: Isolate the variable (c)", "Subtract (\frac{70}{3}) from both sides:", "[\nc = -4 - \frac{70}{3}\n]", "Convert (-4) into a fraction with denominator 3:", "[\nc = -\frac{12}{3} - \frac{70}{3} = -\frac{82}{3}\n]", "---", "### Final Answer", "[\n\boxed{c = -\frac{82}{3}}\n]", "---", "### Key Takeaways", "- Simplifying fractions reduces complexity in equations.\n- Always combine like terms before isolating variables.\n- Converting whole numbers to fractions with a common denominator is essential for accurate arithmetic.\n- This method builds a clear path to solving linear equations involving fractions.", "---", "### Why This Equation Matters", "Understanding how to solve equations like (-\frac{49}{6} + \frac{189}{6} + c = -4) is foundational for algebra. Such problems appear in science, engineering, and economics where fractional changes and balance equations are common. Mastery of fraction operations and linear isolation ensures you're prepared for more advanced math challenges.", "---", "Keywords:, solve algebra equation, combining fractions, linear equations with fractions, algebraic steps, solving for variable c, (-\frac{49}{6} + \frac{189}{6} + c = -4*, step-by-step math tutorial, fraction arithmetic, algebra solving guide"]