First, solve the second equation for \( p \):

["Title: How to Solve the Second Equation for ( p ): A Step-by-Step Guide", "When solving equations in algebra, especially in systems of equations, isolating one variable at a time is a fundamental strategy that makes problems more manageable. In this article, we focus on one key step: solving the second equation for ( p ). Understanding this process empowers you to tackle complex equations confidently and lays the groundwork for more advanced problem-solving.", "---", "### Understanding the Second Equation", "Consider a linear equation involving ( p ), such as:", "[\n2p + 3q = 12\n]", "To solve this for ( p ), our goal is to isolate ( p ) on one side. The first step is to eliminate other variables or terms from that side, using inverse operations.", "---", "### Step 1: Solve the Second Equation for ( p )", "Start with the equation:", "[\n2p + 3q = 12\n]", "Subtract ( 3q ) from both sides to isolate the term with ( p ):", "[\n2p = 12 - 3q\n]", "Now divide both sides by 2 to solve for ( p ):", "[\np = \frac{12 - 3q}{2}\n]", "This expression gives ( p ) entirely in terms of ( q ), making it easy to substitute into another equation or analyze independently.", "---", "### Why This Matters", "Solving for ( p ) in the second equation is often a critical step when working with systems of equations. Once you express ( p ) in terms of the other variable (here ( q )), you can:", "- Substitute into the first equation forward-substitute.\n- Solve the combined system more efficiently.\n- Analyze relationships between variables.", "---", "### Tips for Mastering This Skill", "- Balance the equation: What you do to one side, do to the other.\n- Use inverse operations: Add/subtract to eliminate terms, multiply/divide to isolate variables.\n- Simplify first, then isolate: Reduce expressions before solving.\n- Check your work: Plug your value of ( p ) back into the original equation to verify.", "---", "### Real-World Application Example", "Suppose you’re analyzing a scenario where ( p ) represents profit per unit and ( q ) is the number of units sold. Knowing how to solve for ( p ) helps business analysts determine pricing strategies based on expected sales revenue.", "---", "### Conclusion", "Mastering how to solve the second equation for ( p ) is a crucial skill in algebra. It builds confidence in handling multiple equations and paves the way for solving systems, graphing linear relationships, and modeling real-world problems. Start with isolating ( p ), practice with different equations, and soon you’ll solve these steps instinctively.", "---", "Track this topic for more guides on solving equations, systems of equations, and algebra essentials. Stay tuned for detailed walkthroughs and practical applications!", "---", "Keywords: solve second equation for p, how to isolate p in equation, algebra step-by-step, equation solving tutorial, linear equations, p in equation, mathematics practice, solving for a variable, intermediate algebra."]