$8(p+2)-3[\{(3-2 p)-3(-3 p-5)\}]=0$
Answer (1)
Simplify the innermost parentheses: − 3 ( − 3 p − 5 ) = 9 p + 15 .
Simplify the expression inside the curly brackets: ( 3 − 2 p ) + ( 9 p + 15 ) = 7 p + 18 .
Substitute back into the equation and expand: 8 ( p + 2 ) − 3 [ 7 p + 18 ] = 8 p + 16 − 21 p − 54 = 0 .
Combine like terms and solve for p : − 13 p − 38 = 0 , so p = − 13 38 .
Explanation
Analyze the problem We are given the equation 8 ( p + 2 ) − 3 [{( 3 − 2 p ) − 3 ( − 3 p − 5 )}] = 0 and we want to solve for p . Let's break down the equation step by step.
Simplify innermost parentheses First, we simplify the expression inside the innermost parentheses: − 3 ( − 3 p − 5 ) = 9 p + 15 .
Simplify curly brackets Now, substitute this back into the curly brackets: ( 3 − 2 p ) − 3 ( − 3 p − 5 ) = ( 3 − 2 p ) + ( 9 p + 15 ) = 3 − 2 p + 9 p + 15 = 7 p + 18 .
Substitute back into the equation Next, substitute this back into the equation: 8 ( p + 2 ) − 3 [ 7 p + 18 ] = 0 .
Expand the terms Expand the terms: 8 p + 16 − 21 p − 54 = 0 .
Combine like terms Combine like terms: ( 8 p − 21 p ) + ( 16 − 54 ) = − 13 p − 38 = 0 .
Isolate p Isolate p : − 13 p = 38 .
Solve for p Finally, solve for p : p = − 13 38 .
Final Answer Therefore, the solution to the equation is p = − 13 38 .
Examples
Imagine you're adjusting a recipe that involves multiple ingredients and steps. If you need to scale the recipe up or down, you'll encounter similar algebraic expressions. Solving for a variable like 'p' in this equation is akin to finding the right amount of an ingredient to maintain the recipe's balance. This skill is also useful in budgeting, where you might need to calculate expenses and income to find a balanced financial plan. Understanding how to manipulate and solve equations helps in many practical situations where you need to find the right value to achieve a desired outcome.
