$ \Rightarrow \frac{-98 + 297}{3} + c = -4 \Rightarrow \frac{199}{3} + c = -4 \Rightarrow c = -4 - \frac{199}{3} = -\frac{211}{3} $
["Solving the Equation: Step-by-Step Explanation of $ c = -\frac{211}{3} $", "Understanding how to solve linear equations step by step is essential for mastering algebra. In this article, we’ll break down the equation $ \frac{-98 + 297}{3} + c = -4 \Rightarrow \frac{199}{3} + c = -4 $, showing how to isolate and solve for $ c $. The final result is $ c = -\frac{211}{3} $, a clean and precise solution with clear reasoning.", "---", "### Step 1: Simplify the Numerator Inside the Fraction", "Start with the original expression:", "$$\n\frac{-98 + 297}{3} + c = -4\n$$", "Combine the terms in the numerator:", "$$\n-98 + 297 = 199\n$$", "Now the equation becomes:", "$$\n\frac{199}{3} + c = -4\n$$", "---", "### Step 2: Isolate the Variable $ c $", "Subtract $ \frac{199}{3} $ from both sides to isolate $ c $:", "$$\nc = -4 - \frac{199}{3}\n$$", "To perform the subtraction, express $ -4 $ as a fraction with denominator 3:", "$$\n-4 = -\frac{4 \cdot 3}{3} = -\frac{12}{3}\n$$", "Now rewrite the equation:", "$$\nc = -\frac{12}{3} - \frac{199}{3}\n$$", "---", "### Step 3: Combine the Fractions", "Since the denominators are the same, subtract the numerators:", "$$\nc = -\left( \frac{12 + 199}{3} \right) = -\frac{211}{3}\n$$", "---", "### Final Result", "$$\n\boxed{ c = -\frac{211}{3} }\n$$", "This solution shows how combining constants and expressing negative integers as fractions enables accurate arithmetic in algebra. Recognizing this step-by-step process makes solving equations clearer and more intuitive, whether for homework, standardized tests, or real-world applications involving linear relationships.", "---", "Key SEO Keywords:\nLinear equations, solving for c, algebra solution steps, fractions in equations, automated equation solving, linear algebra tutorial, step-by-step math problems, $ c = -\frac{211}{3} $, algebraic isolation technique", "---", "Try solving similar equations today and reinforce your mathematical confidence!"]
