\[ 10b - 3 = 12 \] - Dygne

["# Solving (10b - 3 = 12): A Step-by-Step Guide", "If you're working through an algebraic equation like (10b - 3 = 12), you're tackling a common linear equation that forms the foundation of algebra. Whether you're a student learning basic math or someone brushing up on fundamental problem-solving skills, understanding how to solve this equation can strengthen your math proficiency.", "## What Is the Equation (10b - 3 = 12)?", "The equation (10b - 3 = 12) is a one-step linear equation in a variable (b). It shows a relationship between (b) and numbers, where 10 times (b), minus 3, equals 12. Solving it means finding the value of (b) that makes both sides equal.", "## How to Solve (10b - 3 = 12)", "Here’s a clear, step-by-step way to solve the equation:", "1. Start with the original equation:
\n [
\n 10b - 3 = 12
\n ]", "2. Add 3 to both sides to isolate the term with (b):
\n [
\n 10b - 3 + 3 = 12 + 3
\n ]
\n Simplifying:
\n [
\n 10b = 15
\n ]", "3. Divide both sides by 10 to solve for (b):
\n [
\n b = \frac{15}{10}
\n ]
\n Simplifying the fraction:
\n [
\n b = 1.5
\n ]
\n Alternatively, as a fraction:
\n [
\n b = \frac{3}{2} \quad \ ext{or} \quad b = 1 \frac{1}{2}
\n ]", "## Final Answer", "[
\n\boxed{b = 1.5}
\n]
\nor
\n[
\n\boxed{b = \frac{3}{2}}
\n]", "## Why This Matters", "Solving equations like (10b - 3 = 12) builds key algebraic thinking:", "- Translating word problems into mathematical expressions
\n- Using inverse operations to isolate variables
\n- Confirming solutions by substituting back into the original equation", "Such equations form building blocks for more complex mathematics, including science, engineering, and economics.", "## Practice Tips", "- Try similar equations: substitute different numbers to reinforce skill
\n- Solve equations step-by-step without skipping logic
\n- Check your answer by plugging (b = 1.5) back in:
\n [
\n 10(1.5) - 3 = 15 - 3 = 12 \quad \ ext{(Correct!)}
\n ]", "## Conclusion", "Mastering linear equations is a powerful skill. The solution to (10b - 3 = 12)—(b = 1.5)—is simple yet essential. Keep practicing, and you’ll build confidence for advanced math and real-world problem-solving.", "---", "Keywords: solve 10b - 3 = 12, algebra basics, linear equation solution, how to solve 10b - 3 = 12, step-by-step algebra, value of b in equations, linear equations for beginners"]