7(2889) + 3(-17316) + c = 38 \Rightarrow 20223 - 51948 + c = 38 \Rightarrow c = 31725
["Understanding the Equation: Solving for ( c ) in 7(2889) + 3(-17316) + c = 38", "Mathematics often involves manipulating equations step by step to isolate unknown variables — a process essential for students, educators, and anyone working with algebra. In this article, we dive into a specific equation:", "[\n7(2889) + 3(-17316) + c = 38\n]", "and walk through how to solve for ( c ), arriving at the final result:\n[\nc = 31725\n]", "---", "### Step 1: Simplify the Left Side of the Equation", "Begin by calculating the known products on the left-hand side.", "Compute ( 7 \ imes 2889 ):\n[\n7 \ imes 2889 = 20223\n]", "Compute ( 3 \ imes (-17316) ):\n[\n3 \ imes (-17316) = -51948\n]", "Now rewrite the original equation with these values substituted:", "[\n20223 - 51948 + c = 38\n]", "---", "### Step 2: Combine the Constant Terms", "Add or subtract the constants on the left:", "[\n20223 - 51948 = -31725\n]", "So the equation becomes:", "[\n-31725 + c = 38\n]", "---", "### Step 3: Isolate the Variable ( c )", "To solve for ( c ), add 31725 to both sides:", "[\nc = 38 + 31725\n]", "[\nc = 31725\n]", "---", "### Final Result", "[\n\boxed{c = 31725}\n]", "This straightforward algebraic process highlights how combining like terms and isolating the variable allows us to confidently compute unknown values. Whether learning, teaching, or solving real-world problems, mastering such steps builds a strong foundation in mathematical reasoning.", "Key Takeaways:", "- Always simplify each term before combining\n- Use inverse operations to isolate the variable\n- Never skip steps — even basic arithmetic matters", "Understanding and solving equations like this empowers you to tackle more complex problems with clarity and precision.", "---", "Related Topics:\n- Linear Equations\n- Algebraic Manipulation\n- Solving for Variables\n- Step-by-step Algebra Tutorials", "Keywords: solve for c, algebraic equation, 7×2889 + 3×(-17316), isolate variable, step-by-step solving, c = 31725, math tutorial, algebra practice."]
