Solve the second equation for \( p \): \( 2p = 14 - 3n \) → \( p = 7 - 1.5n \)

["Solving the Equation: How to Find ( p ) in Terms of ( n )", "When solving linear equations, one of the most common tasks is isolating the desired variable—here, that variable is ( p ). Consider the equation:", "[\n2p = 14 - 3n\n]", "To solve for ( p ), follow simple algebraic steps to isolate it. Each step preserves the equation’s equality while transforming it into a clearer, usable form.", "---", "### Step-by-Step Solution", "Start with the original equation:", "[\n2p = 14 - 3n\n]", "To eliminate the coefficient ( 2 ) multiplying ( p ), divide both sides of the equation by 2:", "[\np = \frac{14 - 3n}{2}\n]", "This expression can be split into two terms:", "[\np = \frac{14}{2} - \frac{3n}{2}\n]", "Simplifying each term gives:", "[\np = 7 - 1.5n\n]", "---", "### Final Answer", "Thus, solving for ( p ) yields:", "[\np = 7 - 1.5n\n]", "---", "### Why This Matters: Applications and Understanding", "Rewriting equations like this is vital in algebra, particularly in modeling real-world scenarios. For example, in budgeting, economics, or physics, variables often depend linearly on each other. Expressing ( p ) explicitly in terms of ( n ) enables easier substitution, graphing, or numerical analysis.", "---", "### Understanding the Coefficients", "- The constant ( +7 ) reflects the fixed component when ( n = 0 ).\n- The term ( -1.5n ) shows how ( p ) decreases as ( n ) increases, highlighting the inverse relationship.", "---", "In summary, solving ( 2p = 14 - 3n ) for ( p ) results in ( p = 7 - 1.5n ), a clean linear expression showing how ( p ) varies with ( n ). This step-based approach is fundamental in algebra and prepares learners for more complex equation-solving tasks."]