Solve for \( y \) in the equation \( 5y - 7 = 3y + 9 \).

["# Solving for ( y ) in the Equation ( 5y - 7 = 3y + 9 )", "Mastering algebraic equations is a fundamental skill for students and aspiring mathematicians. One classic problem often used to build foundational algebra skills is solving for ( y ) in a linear equation like ( 5y - 7 = 3y + 9 ). This article walks you through the step-by-step process of solving this equation clearly and effectively, offering practical tips and explaining key algebra concepts.", "## Understanding the Equation", "The equation ( 5y - 7 = 3y + 9 ) is a linear equation in one variable, ( y ). It contains equal signs, meaning the expression on the left equals the expression on the right. Our goal is to isolate ( y ) on one side to find its value.", "## Step-by-Step Solution", "### Step 1: Eliminate Variable Terms from One Side", "To solve for ( y ), start by moving all terms with ( y ) to one side of the equation. Subtract ( 3y ) from both sides:\n[\n5y - 7 - 3y = 3y + 9 - 3y\n]\nSimplifying both sides gives:\n[\n2y - 7 = 9\n]", "### Step 2: Isolate the Variable Term", "Now, eliminate the constant term on the left by adding 7 to both sides:\n[\n2y - 7 + 7 = 9 + 7\n]\nSimplifying:\n[\n2y = 16\n]", "### Step 3: Solve for ( y )", "Finally, divide both sides by 2 to isolate ( y ):\n[\n\frac{2y}{2} = \frac{16}{2}\n]\n[\ny = 8\n]", "## Final Answer", "After carefully following each step—moving like terms together, isolating the variable, and simplifying—we find that:\n[\n\boxed{y = 8}\n]", "## Verification: Plugging Back to Check", "To confirm the solution is correct, substitute ( y = 8 ) into the original equation:\nLeft side: ( 5(8) - 7 = 40 - 7 = 33 )\nRight side: ( 3(8) + 9 = 24 + 9 = 33 )\nSince both sides equal 33, the solution ( y = 8 ) is verified.", "## Why This Equation Matters in Real Learning", "Understanding how to solve ( 5y - 7 = 3y + 9 ) builds core algebra skills such as combining like terms, maintaining equation balance, and isolating variables. These abilities are essential for tackling more complex equations and are widely applicable in science, engineering, and economics.", "---", "### Key Takeaways\n- Balance the equation by performing the same operation on both sides.\n- Group variable terms on one side and constants on the other.\n- Simplify using basic arithmetic to isolate the variable.\n- Always verify your solution by substituting back into the original equation.", "Mastering these steps transforms algebraic problem-solving from a daunting task into a clear, manageable process—one that strengthens numerical reasoning for years to come."]