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9. \( 2(p+5)+3 p=25 \)

Ask by Gonzalez Franklin. in the United States
Jan 23,2025

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Tutor-Verified Answer

Answer

\( p=3 \)

Solution

Solve the equation \( 2(p+5)+3p=25 \). Solve the equation by following steps: - step0: Solve for \(p\): \(2\left(p+5\right)+3p=25\) - step1: Move the expression to the left side: \(2\left(p+5\right)+3p-25=0\) - step2: Calculate: \(5p-15=0\) - step3: Move the constant to the right side: \(5p=0+15\) - step4: Remove 0: \(5p=15\) - step5: Divide both sides: \(\frac{5p}{5}=\frac{15}{5}\) - step6: Divide the numbers: \(p=3\) The solution to the equation \(2(p+5)+3p=25\) is \(p=3\).

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Bonus Knowledge

To solve the equation \( 2(p+5)+3p=25 \), start by distributing the 2: \( 2p + 10 + 3p = 25 \). Combine like terms: \( 5p + 10 = 25 \). Next, subtract 10 from both sides: \( 5p = 15 \). Finally, divide by 5: \( p = 3 \). Now you've got the value of \( p \)! The beauty of solving equations like this is that they form the foundation for more complex mathematics. Whether you're prepping for algebra tests or doing real-life budgeting, these skills are like your algebraic superpower! The satisfaction of finding the unknown variable is like solving a mystery—you never know what you might discover along the way! In real-world scenarios, this problem setup could relate to budgeting, where \( p \) represents factors in your expenses. Just as in solving for variables, balancing budgets often means breaking down costs, combining like terms (expenses), and figuring out how to allocate your resources efficiently. Apply this method to plan your finances—before you know it, you’ll be the financial whiz among your friends!

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