["# Solving 3a – 5 = 2(4 – a): A Step-by-Step Guide
\nMaster Algebra Quickly & Confidently | 3A – 5 = 2(4 – a)", "Ever found yourself staring at the equation 3a – 5 = 2(4 – a), feeling confused about where to begin? You’re not alone — algebraic equations like this one are common in math class and essential to master. In this article, we’ll break down how to solve 3a – 5 = 2(4 – a) step by step, helping you understand the process confidently and efficiently.", "## Why Learning This Equation Matters", "Understanding linear equations is foundational in algebra. Solving equations like 3a – 5 = 2(4 – a) helps develop problem-solving skills and prepares you for more complex math topics like functions, graphing, and real-world applications in science and engineering.", "---", "## Step 1: Expand the Right-Hand Side", "Start by distributing the 2 on the right side of the equation:", "[
\n3a – 5 = 2 \cdot 4 – 2 \cdot a
\n]", "[
\n3a – 5 = 8 – 2a
\n]", "---", "## Step 2: Move All Terms with the Variable to One Side", "Add 2a to both sides to gather all terms involving a on the left:", "[
\n3a + 2a – 5 = 8
\n]", "[
\n5a – 5 = 8
\n]", "---", "## Step 3: Isolate the Variable Term", "Add 5 to both sides:", "[
\n5a = 8 + 5
\n]", "[
\n5a = 13
\n]", "---", "## Step 4: Solve for a", "Divide both sides by 5:", "[
\na = \frac{13}{5}
\n]", "or in decimal form:", "[
\na = 2.6
\n]", "---", "## Final Answer", "[
\n\boxed{a = \frac{13}{5}}
\n]", "---", "## Quick Check: Verify the Solution", "To ensure correctness, substitute a = 13/5 back into the original equation:", "Left side:
\n[
\n3\left(\frac{13}{5}\right) – 5 = \frac{39}{5} – 5 = \frac{39}{5} – \frac{25}{5} = \frac{14}{5}
\n]", "Right side:
\n[
\n2\left(4 – \frac{13}{5}\right) = 2\left(\frac{20}{5} - \frac{13}{5}\right) = 2\left(\frac{7}{5}\right) = \frac{14}{5}
\n]", "Both sides equal 14/5, confirming our solution is correct.", "---", "## Summary", "- Distribute and expand first
\n- Collect like terms
\n- Isolate the variable term
\n- Solve step by step
\n- Verify by plugging back in", "Mastering this process turns tricky equations into clear, manageable steps. Whether for homework, standardized tests, or building algebraic intuition, understanding 3a – 5 = 2(4 – a) makes solving similar linear equations straightforward and fast.", "---", "### Want more algebra tips?
\nCheck out our guides on solving linear equations, combining like terms, and verifying solutions — all designed to boost your math confidence!", "---", "Keywords:
\nalgebra equation, solve 3a – 5 = 2(4 – a), linear equation, step-by-step, math tutoring, solving equations, algebra practice", "Meta Description:
\nLearn how to solve 3a – 5 = 2(4 – a) step by step. Master linear equations with clear, easy-to-follow instructions including expansion, isolating variables, and verifying solutions. Perfect for students and self-learners!"]
