Now substitute \( b = \frac{3}{2} \) back into \( a = 2b - 1 \):
["SEO Article: Solving for ( a ) by Substituting ( b = \frac{3}{2} ) into ( a = 2b - 1 ) – Step-by-Step Explanation", "When solving for ( a ) in the equation ( a = 2b - 1 ), substituting a specific value for ( b ) streamlines the process and clarifies the final result. In this guide, we’ll walk through the step-by-step substitution of ( b = \frac{3}{2} ) into the equation ( a = 2b - 1 ), making the math both accessible and practical for learners, students, and anyone interested in algebra.", "---", "### Understanding the Equation", "The original equation is:\n[\na = 2b - 1\n]\nHere, ( a ) depends directly on ( b ). To find the specific value of ( a ), we must substitute the known value of ( b = \frac{3}{2} ) into the expression.", "---", "### Step 1: Plugging in the Value", "Substitute ( b = \frac{3}{2} ) into the formula:\n[\na = 2 \left( \frac{3}{2} \right) - 1\n]", "---", "### Step 2: Multiply First", "Compute the multiplication:\n[\n2 \ imes \frac{3}{2} = \frac{6}{2} = 3\n]", "So now the equation becomes:\n[\na = 3 - 1\n]", "---", "### Step 3: Subtract to Solve", "Perform the subtraction:\n[\na = 2\n]", "---", "### Final Result", "After substituting ( b = \frac{3}{2} ) into ( a = 2b - 1 ), we find:\n[\n\boxed{a = 2}\n]", "This example illustrates how quickly substitution simplifies solving for one variable in a linear equation—especially when dealing with fractions, which are common in algebraic contexts.", "---", "### Why This Matters for Beginners and Tutors", "Substituting known values is a foundational skill in algebra. It helps students:", "- Reinforce understanding of direct proportionality\n- Practice simplifying expressions with fractions\n- Build confidence in handling variables and arithmetic operations\n- Prepare for more complex equations involving substitution and elimination", "Whether you're a high school student mastering algebra or a tutor teaching foundational concepts, mastering this technique accelerates learning and improves problem-solving efficiency.", "---", "### TL;DR:\nTo solve ( a = 2b - 1 ) when ( b = \frac{3}{2} ):\nSubstitute ( b ):\n[\na = 2 \left( \frac{3}{2} \right) - 1 = 3 - 1 = 2\n]\nSo, ( \boxed{a = 2} )", "---", "Related Keywords for SEO:\n- How to substitute values in equations\n- Step-by-step algebra substitution\n- Solve linear equations by substitution\n- Fraction substitution in algebra\n- Equation solving practice problems", "---", "Optimizing mathematical explanations with clear substitution examples helps students grasp core concepts faster. Use this structured approach whenever solving for one variable in a linear formula—just substitute, simplify, and solve with confidence!"]
