Problem 74 Clear parentheses and combine li... [FREE SOLUTION]

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Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

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Chapter 3: Problem 74

Clear parentheses and combine like terms. $$7(a-4)+8$$

Short Answer

Expert verified

7a - 20

Step by step solution

- Distribute the 7

Apply the distributive property by multiplying 7 with both terms inside the parentheses: 7(a - 4) becomes 7a - 28.

- Add the constant

Combine the term outside the parentheses with the simplified expression: 7a - 28 + 8. Now combine the constants (-28 and 8).

- Combine Like Terms

Combine -28 and 8 to get -20: The simplified expression is 7a - 20.

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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 prealgebra. It's used when you need to multiply a single term by each term inside a set of parentheses. This property helps break down more complicated expressions into simpler ones. For instance, in the expression $7(a - 4)$, you distribute the 7 to both $a$ and $-4$,
This means:

7 times $a$
7 times $-4$

So, after applying the distributive property, $7(a - 4)$ becomes $7a - 28$, making the expression easier to handle. Remembering this property will help you simplify many expressions quickly.

Combine Like Terms

Combining like terms is another essential skill. It helps to simplify expressions by adding or subtracting terms that have identical variable parts. For example, in the expression $7a - 28 + 8$, we identify the like terms:

$7a$ (The variable term)
$-28$ and $8$ (The constant terms)

Since $7a$ doesn鈥檛 have any other 'a' term to combine with, it stays the same. Next, you combine the constants. So, $-28 + 8$ becomes $-20$. The simplified expression is now $7a - 20$. Practicing how to combine like terms can greatly streamline simplification processes.

Simplifying Expressions

When we talk about simplifying expressions, we mean rewriting them in their simplest form. This often involves both applying the distributive property and combining like terms. Here's how it works through an example:

Start with the expression: $7(a - 4) + 8$.
First, use the distributive property: $7a - 28$.
Add the constant term: $7a - 28 + 8$.
Combine like terms: $-28 + 8 = -20$.

You end up with the simplified expression $7a - 20$. By understanding and using these steps, you can simplify many expressions efficiently. Simplifying expressions makes them easier to understand and work with.

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91影视

Clear parentheses and combine like terms. $$7(a-4)+8$$

Short Answer

Step by step solution

- Distribute the 7

- Add the constant

- Combine Like Terms

Key Concepts

Distributive Property

Combine Like Terms

Simplifying Expressions

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