Simplify: \( 12x + 12 = 78 \) → \( 12x = 66 \) → \( x = 5.5 \)

["# Solving Linear Equations: Step-by-Step Guide to Simplify ( 12x + 12 = 78 )", "Understanding how to solve linear equations is a fundamental skill in algebra, laying the foundation for more complex mathematical concepts. One classic example is simplifying the equation:\n( 12x + 12 = 78 ) → ( 12x = 66 ) → ( x = 5.5 )", "This straightforward equation demonstrates solving for ( x ) using basic algebraic operations. In this article, we break down each step clearly so you can easily follow and apply the method in similar problems.", "---", "## What Is the Equation?", "We begin with:\n[ 12x + 12 = 78 ]\nOur goal is to isolate ( x ) and find its value.", "---", "## Step 1: Subtract 12 from Both Sides to Eliminate the Constant Term", "To begin solving, we remove the 12 on the left side by subtracting 12 from both sides:\n[\n12x + 12 - 12 = 78 - 12\n]\nSimplifying both sides gives:\n[ 12x = 66 ]", "This step uses the addition property of equality, which ensures the equation stays balanced by performing the same operation on both sides.", "---", "## Step 2: Divide Both Sides by 12 to Solve for ( x )", "Next, divide both sides by 12 to isolate ( x ):\n[\n\frac{12x}{12} = \frac{66}{12}\n]\nThis simplifies to:\n[ x = \frac{66}{12} ]", "To express the answer clearly, reduce the fraction:\n[ \frac{66 \div 6}{12 \div 6} = \frac{11}{2} ]\nor in decimal form:\n[ x = 5.5 ]", "---", "## Why Is the Decimal Equivalent Handy?", "Expressing ( x = 5.5 ) shows that the solution is a non-integer value, highlighting the importance of understanding fractions and decimals in algebra. While algebra often begins with whole numbers, real-world problems frequently involve fractions and decimals — making this conversion essential for practical applications.", "---", "## Summary of Steps", "- Start with: ( 12x + 12 = 78 )\n- Subtract 12 from both sides: ( 12x = 66 )\n- Divide both sides by 12: ( x = 5.5 )", "---", "## Real-World Applications of Solving Linear Equations", "Linear equations like ( 12x + 12 = 78 ) appear in diverse fields:", "- Budgeting and finance: Calculating break-even points or monthly savings.\n- Science: Determining rates of change in experiments.\n- Everyday life: Finding unknown quantities such as time, distance, or ratios.", "---", "## Practice Problem", "Try solving your own:\n[ 12x + 12 = 78 ]\nFollowing the same steps will lead you to the same solution, reinforcing the method’s reliability.", "---", "## Conclusion", "Solving the equation ( 12x + 12 = 78 ) is a straightforward but vital exercise in algebraic reasoning. By simplifying step-by-step — subtracting and then dividing — and converting to decimal form when needed, you master essential skills for advancing in mathematics. Whether you're solving equations for school, work, or personal projects, clear, logical steps ensure accuracy and confidence.", "---", "### Keywords for SEO Optimization:\nlinear equations, algebra beginner, solve 12x + 12 = 78, step-by-step equation solving, divide both sides, simplify algebra, decimals in algebra, real-world equations, break-even point, math tutorial"]