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Chapter 7: Problem 132

In the following exercises, simplify using the distributive property. $$(5 m-3)-(m+7)$$

Short Answer

Expert verified
4m - 10

Step by step solution

01

Identify Terms Inside Parentheses

Recognize the terms inside the parentheses in the expression \( (5m - 3) - (m + 7) \).
02

Distribute the Negative Sign

Distribute the negative sign to each term inside the second set of parentheses: \(5m - 3 - m - 7\).
03

Combine Like Terms

Combine the like terms: \(5m - m - 3 - 7 = 4m - 10\).

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Key Concepts

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

Simplifying Algebraic Expressions
When simplifying algebraic expressions, your goal is to make the expression as simple as possible. Typically, this process involves combining like terms and distributing any constants or variables. In the expression \((5m - 3) - (m + 7)\), following these steps can help:

1. Identify terms inside parentheses: \((5m - 3) - (m + 7)\).
2. Distribute the negative sign: \(5m - 3 - m - 7\).
3. Combine like terms: \(5m - m - 3 - 7 = 4m - 10\).

Remember, simplifying expressions helps you understand the relationship between the variables and constants more clearly.
Combining Like Terms
Combining like terms is a crucial step in simplifying algebraic expressions. Like terms are terms that have the same variable raised to the same power. For instance, in the expression \(5m - 3 - m - 7\), the like terms are \(5m\) and \(-m\).

To combine these like terms, you simply add or subtract their coefficients. Here, \(5m - m = 4m\). The constants \(-3\) and \(-7\) are also like terms and can be combined: \(-3 - 7 = -10\).

After combining like terms, the expression becomes \(4m - 10\). It's simpler and easier to work with.
Negative Sign Distribution
Distributing a negative sign is an essential skill in algebra. When you have an expression like \((5m - 3) - (m + 7)\), the negative sign affects every term inside the parentheses it precedes. This step is crucial to avoid common mistakes.

Consider the expression \(-(m + 7)\). Distributing the negative sign, we get \(-m - 7\).

Notice how each term inside the parentheses changes its sign. Adding these modified terms back into the original expression, we obtain \(5m - 3 - m - 7\).

Properly distributing the negative sign is key to correctly simplifying algebraic expressions.

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Most popular questions from this chapter

In the following exercises, simplity using the distributive property. $$ -3(6 m-1) $$

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