Solve for \(r\): \(20(1 - r) = 5\), \(20 - 20r = 5\), \(20r = 15\), \(r = 0.75\).
["How to Solve the Equation: $ 20(1 - r) = 5 $ – Step-by-Step Explanation", "Solving linear equations is a fundamental skill in algebra, and mastering a simple process like isolating the variable can help you tackle more complex problems with confidence. In this article, we’ll walk through the complete solution to the equation:\n$$\n20(1 - r) = 5\n$$\nand explain each step clearly.", "---", "### Step 1: Expand the Left Side", "We begin by distributing the 20 across the parentheses:\n$$\n20(1 - r) = 20 \cdot 1 - 20 \cdot r = 20 - 20r\n$$\nSo the equation becomes:\n$$\n20 - 20r = 5\n$$", "---", "### Step 2: Isolate the Term With ( r )", "To solve for ( r ), we first subtract 20 from both sides to move the constant to the right:\n$$\n20 - 20r - 20 = 5 - 20\n$$\nSimplifying both sides gives:\n$$\n-20r = -15\n$$", "---", "### Step 3: Solve for ( r )", "Now divide both sides by (-20):\n$$\nr = \frac{-15}{-20} = \frac{15}{20} = 0.75\n$$", "---", "### Final Result", "The solution to the equation ( 20(1 - r) = 5 ) is:\n$$\n\boxed{r = 0.75}\n$$", "---", "### Why This Matters in Real-World Contexts", "Equations like this appear in finance, physics, and engineering when balancing costs, growth rates, or proportions. Understanding how to isolate variables empowers you to model and solve real-life problems efficiently.", "---", "### Summary of Key Algebra Steps:\n1. Expand: Distribute coefficients.\n2. Transpose: Move constants to one side.\n3. Divide: Isolate the variable.", "Mastering these steps makes solving algebra challenging — and satisfying — a skill you’ll use every day. Try solving similar equations to build fluency!"]
