\[ 7(1) + 3(1) + r = 11 \Rightarrow 7 + 3 + r = 11 \Rightarrow r = 1 \]

["Solving the Equation: 7(1) + 3(1) + r = 11 — Step-by-Step Explanation", "Are you looking to understand how to solve a simple algebraic equation step-by-step? One common problem students and learners face is:", "7(1) + 3(1) + r = 11", "At first glance, this equation might seem straightforward, but mastering each step will strengthen your algebra foundation. In this article, we’ll walk through solving:", "7(1) + 3(1) + r = 11", "step by step, ensuring clarity and understanding — resulting in:", "r = 1", "---", "### Step 1: Simplify the Known Terms", "Begin by calculating the products on the left-hand side.", "The equation is:", "7(1) + 3(1) + r = 11", "Since (1 \ imes 7 = 7) and (1 \ imes 3 = 3), we simply add:", "7 + 3 = 10", "Now the equation becomes:", "10 + r = 11", "---", "### Step 2: Isolate the Variable ( r )", "To solve for ( r ), subtract 10 from both sides of the equation:", "10 + r − 10 = 11 − 10", "This simplifies to:", "r = 1", "---", "### Why This Works", "This problem demonstrates the fundamental algebraic principle of simplifying expressions and isolating variables. By first evaluating constants and then applying inverse operations (subtraction), weeriate the process of solving linear equations cleanly.", "---", "### Final Answer", "[\n\boxed{r = 1}\n]", "---", "### Use This Method for Similar Problems", "Whenever you encounter an equation like A(1) + B(1) + r = C, remember:", "1. Evaluate coefficient × 1 → just leave the number.\n2. Add the constants.\n3. Use inverse operations to isolate ( r ).", "This approach applies to any linear equation with variable ( r ).", "---", "#### Additional Tips", "- Always simplify multiplication before adding.\n- Use one operation per step to keep logic clear.\n- Always check your solution by substituting ( r = 1 ) back into the original equation:", "7(1) + 3(1) + 1 = 7 + 3 + 1 = 11 — ✔️ Correct!", "---", "Mastering these steps helps with more complex algebra and builds confidence in solving equations. Start practicing daily — soon, solving equations like this will feel second nature!", "---", "Keywords: algebra equation solve, how to solve 7(1)+3(1)+r=11, step-by-step linear equations, solve for r, simple algebra, equation practice, r = 1, solving equations tutorial, mathematics fundamentals"]