Problem 9 Simplify each expression. $$ ... [FREE SOLUTION]

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Beginning Algebra

Margaret L. Lial, John Hornsby

$Math Studyset 91影视 Explanations$ Math

11 Edition

Chapter 1: Problem 9

Simplify each expression. $$ -2-(5-3 p) $$

Short Answer

Expert verified

-7 + 3p

Step by step solution

- Distribute the negative sign

Apply the distributive property to the term $5-3p$ by distributing the negative sign. This means $- (5-3p) = -5 + 3p$.

- Rewrite the expression

After distributing the negative sign, the expression $-2 - (5 - 3p)$ becomes $-2 - 5 + 3p$.

- Combine like terms

Combine the constant terms $-2$ and $-5$ to simplify the expression. $-2 - 5 = -7$. So, the expression now is $-7 + 3p$.

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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 crucial in algebra for simplifying expressions. It states that a term outside the parentheses should be multiplied by each term inside. For instance, in the expression $5 - 3p$, if you have a negative sign outside it, you distribute the negative sign to both terms inside. This changes the expression into $-5 + 3p$. Here鈥檚 a simple way to remember:

$- (a + b) = -a + -b$
$- (a - b) = -a + b$

So, $- (5 - 3p)$ becomes $- 5 + 3 p$. Distributing can help break down complex expressions into more manageable pieces.

Combining like terms

Combining like terms is a method of simplifying an expression. Like terms are terms that have the same variable with the same exponent. For example, in the expression $-2 - 5 + 3p$, $-2$ and $-5$ are like terms because they are both constants (numbers without variables). When combining like terms:

Add or subtract the coefficients of the like terms.
Keep the variable part the same.

So, in the expression $-2 - 5 + 3p$, you combine $-2$ and $-5$ to get $-7$. Your simplified expression then becomes $-7 + 3p$. By combining like terms, expressions become simpler and easier to work with.

Negative sign distribution

Distributing a negative sign through a parenthesis means multiplying each term inside by \-1\. This changes the sign of each term. Consider the expression $- (5 - 3p)$.

When you distribute the negative sign:

$- (5) = -5$
$- (- 3p) = + 3p$

So the expression $- (5 - 3p)$ becomes $- 5 + 3p$. This step is important because it helps in combining terms correctly without making sign errors. Remember, a negative outside a parenthesis changes the sign of all terms inside it.

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91影视

Simplify each expression. $$ -2-(5-3 p) $$

Short Answer

Step by step solution

- Distribute the negative sign

- Rewrite the expression

- Combine like terms

Key Concepts

Distributive property

Combining like terms

Negative sign distribution

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