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Chapter 2: Problem 85

\(2(p+5)-(9+p)=-3\)

Short Answer

Expert verified
p = -4

Step by step solution

01

- Distribute

Distribute the 2 across the term \( p + 5 \) in the equation \( 2(p+5)-(9+p)=-3 \) to get \( 2p + 10 - (9 + p) = -3 \)
02

- Combine like terms

Combine the terms containing \( p \) and the constant terms separately: \( 2p + 10 - 9 - p = -3 \), which simplifies to \( p + 1 = -3 \)
03

- Solve for \( p \)

Isolate the variable \( p \) by subtracting 1 from both sides of the equation: \( p + 1 - 1 = -3 - 1 \), which simplifies to \( p = -4 \)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Distributive Property
The distributive property is a fundamental concept in algebra that states you can distribute multiplication over addition or subtraction in an equation. In this exercise, the equation starts as:

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

To apply the distributive property, multiply the number outside the parentheses by each term inside the parentheses separately. This means multiplying 2 by both \(p\) and 5, giving us:
\(2 * p + 2 * 5 = 2p + 10\).

So our new equation becomes:
\(2p + 10 - (9 + p) = -3\).
Remember to distribute correctly and to keep all sign changes in mind.
Combining Like Terms
Combining like terms involves merging terms that have the same variable raised to the same power. This simplifies the equation and makes it easier to solve. In our equation from the previous section:
\(2p + 10 - 9 - p = -3\).
First, group the terms with \(p\) together and the constant terms together:
\(2p - p\) and \(10 - 9\).
This simplifies to:
\(p + 1\).
So, the equation now looks like:
\(p + 1 = -3\).
It鈥檚 crucial to handle each term correctly to avoid making mistakes.
Isolating the Variable
Isolating the variable means solving for the unknown by getting it alone on one side of the equation. Starting from:
\(p + 1 = -3\),
we need to get rid of the 1 that's added to \(p\). To do this, subtract 1 from both sides of the equation. Remember, whatever you do to one side, you must do to the other:
\(p + 1 - 1 = -3 - 1\).
This simplifies to:
\(p = -4\).
Now, \(p\) is isolated, and the equation is solved!

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Most popular questions from this chapter

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