Solving, \( 2 = 5(1-r) \), \( 2 = 5 - 5r \).

["How to Solve the Equation ( 2 = 5(1 - r) ): Step-by-Step Explanation", "Solving equations is a fundamental skill in algebra, essential not only for academics but also for real-world problem-solving. One common type of equation you may encounter is linear equations involving parentheses, such as:", "[\n2 = 5(1 - r)\n]", "In this article, we’ll walk through how to solve this equation step-by-step, understanding each transformation to build confidence in manipulating algebraic expressions. We’ll also highlight how solving such equations helps in modeling practical situations.", "---", "### Step 1: Understand the Equation", "We start with the equation:\n[\n2 = 5(1 - r)\n]", "This equation states that the number 2 is equal to five times the quantity ( (1 - r) ). Our goal is to isolate the variable ( r ) on one side to determine its value.", "---", "### Step 2: Distribute the 5", "Next, distribute the 5 on the right-hand side:", "[\n2 = 5 \cdot 1 - 5 \cdot r\n]\n[\n2 = 5 - 5r\n]", "Now the equation simplifies to:\n[\n2 = 5 - 5r\n]", "Distributing ensures we express the equation clearly before isolating the variable.", "---", "### Step 3: Isolate the Term With ( r )", "To solve for ( r ), isolate the term containing ( r ). Subtract 5 from both sides:", "[\n2 - 5 = -5r\n]\n[\n-3 = -5r\n]", "By subtracting 5 from both sides, we move the constant term to the left, keeping the equation balanced.", "---", "### Step 4: Solve for ( r )", "Now divide both sides of the equation by (-5):", "[\nr = \frac{-3}{-5} = \frac{3}{5}\n]", "Thus,\n[\nr = \frac{3}{5}\n]", "---", "### Final Answer", "[\n\boxed{r = 0.6 \quad \ ext{or} \quad r = \frac{3}{5}}\n]", "---", "### Why This Matters", "Equations like ( 2 = 5(1 - r) ) model real-life scenarios such as:", "- Budgeting: When 2 dollars meet 5 times a reduction rate ( r ) from a higher value.\n- Physics: Modeling relationships between distance, speed, and time.\n- Finance: Calculating interest rates or depreciation.", "Solving such equations enables precise predictions and informed decision-making.", "---", "### Quick Summary of Key Steps", "| Step | Action |\n|--------------------|----------------------------------------|\n| 1 | Understand the original equation |\n| 2 | Distribute and simplify |\n| 3 | Move constant terms to isolate ( r ) |\n| 4 | Divide to find ( r ) |", "---", "### Practice Idea", "Try solving these similar equations:\n1. ( 7 = 4(1 - x) )\n2. ( 3 = 6 - 3y )\n3. ( 1.5 = 8(1 - z) )", "Apply the same steps: distribute, isolate variable, then solve.", "---", "Mastering basic algebra steps like solving ( 2 = 5(1 - r) ) lays a strong foundation for advanced math and everyday problem-solving. Practice daily to build speed and accuracy!", "---", "Keywords for SEO:\nsolve ( 2 = 5(1 - r) ), step-by-step equation solving, linear equations algebra, algebraic manipulation, how to solve ( 2 = 5 - 5r ), isolation of variables, elementary algebra practice."]