Solve: \( 12(1 - r) = 3 \) → \( 12 - 12r = 3 \) → \( 12r = 9 \) → \( r = rac{3}{4} \).

["Solve the Equation: ( 12(1 - r) = 3 )", "Learning how to solve linear equations is a fundamental skill in algebra, and mastering simple equations like ( 12(1 - r) = 3 ) lays the groundwork for more advanced math. In this detailed guide, we’ll walk through solving ( 12(1 - r) = 3 ) step by step, arriving at the solution ( r = \frac{3}{4} ).", "---", "### Understanding the Equation", "The equation ( 12(1 - r) = 3 ) expresses a real-world scenario where a quantity (like a rate or percentage) is multiplied by a change (1 - r), resulting in a constant value of 3. Our goal is to isolate the variable ( r ) to determine its exact value.", "---", "### Step 1: Expand the Left Side", "First, apply the distributive property (also called expanded form or FOIL method) by distributing 12 to both terms inside the parentheses:", "[\n12(1 - r) = 12 \ imes 1 - 12 \ imes r = 12 - 12r\n]", "Now, rewrite the original equation:", "[\n12(1 - r) = 3 \quad \Rightarrow \quad 12 - 12r = 3\n]", "---", "### Step 2: Isolate the Term with r", "Subtract 12 from both sides to move all constant terms to the right side:", "[\n12 - 12r - 12 = 3 - 12\n]", "This simplifies to:", "[\n-12r = -9\n]", "---", "### Step 3: Solve for r", "Now divide both sides by -12 to isolate ( r ):", "[\nr = \frac{-9}{-12} = \frac{9}{12}\n]", "Simplify the fraction by dividing numerator and denominator by their greatest common divisor, 3:", "[\nr = \frac{3}{4}\n]", "---", "### Summary of Steps", "1. Distribute:\n ( 12(1 - r) = 12 - 12r )\n2. Subtract 12:\n ( 12 - 12r = 3 \Rightarrow -12r = 3 - 12 )\n3. Simplify right side:\n ( -12r = -9 )\n4. Divide by -12:\n ( r = \frac{−9}{–12} = \frac{3}{4} )", "---", "### Why Is This Solution Important?", "The equation ( 12(1 - r) = 3 ) might represent situations involving proportional changes, such as calculating a rate decrease or finding a percentage that satisfies a balance condition. Solving it confirms that when ( r = \frac{3}{4} ), the expression ( 12(1 - r) ) indeed equals 3, validating the arithmetic and logical flow.", "---", "### Final Answer", "[\n\boxed{r = \frac{3}{4}}\n]", "This simple algebraic process illustrates how breaking down the problem step by step leads to a clear and correct solution. Whether for homework, test preparation, or real-life problem-solving, mastering equation solving builds confidence and competence in mathematics.", "---", "### Pro Tips for Practice", "- Always simplify coefficients and fractions completely.\n- Verify your answer by substituting ( r = \frac{3}{4} ) back into the original equation.\n- Practice with similar linear equations to strengthen skill fluency.", "---", "Taglines for SEO:\nSolve linear equations step-by-step\nLearn how to solve ( 12(1 - r) = 3 )\nMaster algebra with real-world problem solving\nAlgebra tutorial: Solve equation and find ( r )"]