Simplify: \(2y + 6 + 3y = 12\), \(5y + 6 = 12\), \(5y = 6\).

["# How to Solve Linear Equations Like (2y + 6 + 3y = 12), (5y + 6 = 12), and (5y = 6\ — A Step-by-Step Guide", "Mathematics is more than numbers—it’s about solving problems step-by-step with clarity. Today, we break down how to simplify and solve common linear equations such as:", "- (2y + 6 + 3y = 12)\n- (5y + 6 = 12)\n- (5y = 6)", "Understanding how these equations work helps build strong problem-solving skills. Let’s walk through each example carefully.", "---", "### Understanding Linear Equations", "A linear equation is an equation that includes variables raised to the first power, arranged in the form (ay + b = c), where (a), (b), and (c) are constants and (y) is the variable. The goal is to isolate the variable on one side of the equation.", "---", "## Step 1: Simplify and Combine Like Terms", "Example: (2y + 6 + 3y = 12)", "Combine like terms (the (y)-terms):\n(2y + 3y = 5y)\nSo, the equation becomes:\n[\n5y + 6 = 12\n]", "This matches the next form:\n[\n5y + 6 = 12\n]", "---", "## Step 2: Isolate the Variable Term", "Subtract 6 from both sides to eliminate the constant:\n[\n5y + 6 - 6 = 12 - 6\n\Rightarrow 5y = 6\n]", "This confirms the last equation:\n[\n5y = 6\n]", "---", "## Step 3: Solve for (y)", "Now, divide both sides by 5:\n[\ny = \frac{6}{5}\n]", "You can express this as a decimal:\n[\ny = 1.2\n]", "---", "## Comparing the Three Equations", "| Equation | Form | Step-by-Step Result |\n|-----------------|------------------------|------------------------|\n| (2y + 6 + 3y = 12) | Combine terms → (5y + 6 = 12) | Subtract 6: (5y = 6), then (y = \frac{6}{5}) |\n| (5y + 6 = 12) | Combine constants | Subtract 6: (5y = 6), then (y = \frac{6}{5}) |\n| (5y = 6) | Isolate variable | Divide by 5: (y = \frac{6}{5}) |", "All three equations follow the same logical path: combine constants, isolate the variable, divide to solve.", "---", "## Why Simplifying Equations Matters", "Solving linear equations builds foundational algebraic reasoning used in science, engineering, economics, and everyday budgeting. Mastering these steps creates confidence in tackling more complex math, such as systems of equations or quadratic models.", "---", "## Final Answer Summary", "Solving:\n(2y + 6 + 3y = 12)\n(\longrightarrow 5y + 6 = 12)\n(\longrightarrow 5y = 6)\n(\longrightarrow y = \frac{6}{5}) or (y = 1.2)", "---", "### Pro Tips for Beginners", "- Always simplify left- and right-hand sides first.\n- Isolate the variable term before dividing.\n- Subtract or add the constant on both sides to keep the equation balanced.\n- Check your answer by plugging (y = \frac{6}{5}) back into the original equation.", "---", "Ready to simplify and solve your next equation? Practice makes perfect! Linear equations are your stepping stones to advanced math mastery.", "---", "Keywords: simplify linear equation, solve 5y = 6, step-by-step algebra, solving equations like 2y + 6 + 3y = 12, how to isolate y, algebra basics, mathematical problem solving"]