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Chapter 7: Problem 128

In the following exercises, simplify using the distributive property. $$22-(a+3)$$

Short Answer

Expert verified
19 - a

Step by step solution

01

- Apply the distributive property

First, distribute the negative sign that is in front of the parenthesis. This involves multiplying each term inside the parenthesis by -1.
02

- Simplify the expression inside the parentheses

Rewrite the expression: $$22 - a - 3.$$
03

- Combine like terms

Combine the constant terms: 22 and -3. This results in: $$19 - a.$$

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Key Concepts

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

Simplification
Simplification in algebra means making an expression easier to work with by performing all possible operations. When simplifying, you work to combine and reduce expressions without changing their value.

In our exercise, this involved simplifying the expression: \(22-(a+3)\).

We distributed the negative sign across the terms inside the parentheses to get: \(22 - a - 3\).

Then, simplification continued by combining like terms, resulting in the final expression: \(19 - a\).
Combining Like Terms
Combining like terms is a key algebraic process where you merge terms that have the same variables and exponents. This helps to simplify expressions and solve equations more easily.

In our example, we originally had the expression \(22 - a - 3\).

Here, 22 and -3 are constants (numbers without variables). To combine these terms, you simply perform the arithmetic operation (subtraction in this case):

  • First, 22 - 3 gives us 19.
This leaves us with the expression: \(19 - a\). The variable term \(-a\) didn't change because it has no like terms to combine with.

Combining like terms makes the expression simpler and more concise.
Parentheses in Algebra
Parentheses in algebra are used to group parts of an expression that need to be worked on first. They indicate which operations to perform before others, following the order of operations (PEMDAS/BODMAS).

In the given exercise, parentheses showed which terms we needed to consider together: \(22-(a+3)\).

We used the distributive property to remove the parentheses by distributing the negative sign across the terms inside them:

  • Distributing the negative sign transformed \(a+3\) into \(-a - 3\).
This allowed us to then simplify the expression to: \(22 - a - 3\).

Removing parentheses correctly is crucial for ensuring accurate simplification and solving of algebraic expressions.

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Most popular questions from this chapter

In the following exercises, use the associative property to rewrite the given expression. (22+7)+3=______

In the following exercises, solve, and state your answer in mixed units. Every day last week, Pedro recorded the amount of time he spent reading. He read for \(50,25,83,45,32,60,\) and 135 minutes. How much time, in hours and minutes, did Pedro spend reading?

In the following exercises, simplify. $$ (n+6.75)+0.25 $$

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Rewrite the expression using the associative property: \((8 \cdot 2) \cdot 5=\)_________
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