Problem 73 Simplify each expression. $$ ... [FREE SOLUTION]

Chapter 1: Problem 73

Simplify each expression. $$ 4 m+6-(m+5) $$

Short Answer

Expert verified

3m + 1

Step by step solution

- Distribute the Negative Sign

Distribute the negative sign through the parentheses. This means changing the signs of all the terms inside the parentheses: 4m + 6 - (m + 5) =4m + 6 - m - 5

- Combine Like Terms

Combine the terms that have the variable 'm' and then the constant terms: 4m - m + 6 - 5 = 3m + 1

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Distributive Property

The distributive property is a key algebraic concept that helps simplify expressions involving parentheses. It allows us to 'distribute' a factor outside the parentheses to each term inside the parentheses.
For example, in the problem $4m + 6 - (m + 5)$, we need to distribute the negative sign through the terms inside the parentheses.
This means we change the signs of all the terms in the parentheses:
\[ 4m + 6 - (m + 5) = 4m + 6 - m - 5 \].
By applying the distributive property correctly, we can simplify and eventually solve the equation correctly.

Combining Like Terms

Combining like terms is an essential step in simplifying algebraic expressions. 'Like terms' are terms that have the same variable raised to the same power. When we combine them, we sum their coefficients.
In our example $4m + 6 - m - 5$, we have:

Two 'm' terms: $4m$ and $-m$
Two constant terms: $6$ and $-5$

To combine like terms, we perform the addition or subtraction of their coefficients:

$4m - m = 3m$
$6 - 5 = 1$

Putting them back together, we get $3m + 1$. This step simplifies the expression further, making it easier to handle.

Algebraic Simplification

Algebraic simplification involves reducing an expression to its simplest form without changing its value. This often requires using the distributive property and combining like terms, along with other algebraic rules.
Let's walk through our example once more: starting with $4m + 6 - (m + 5)$, we distributed the negative sign:
\[ 4m + 6 - m - 5 \].
Next, we combined the like terms by grouping the 'm' terms together and the constant terms together:

First, $4m - m = 3m$
Then, $6 - 5 = 1$

Finally, our fully simplified expression is $3m + 1$.
By mastering these steps, you can simplify any algebraic expression with ease.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Simplify each expression. $$ 4 m+6-(m+5) $$

Short Answer

Step by step solution

- Distribute the Negative Sign

- Combine Like Terms

Key Concepts

Distributive Property

Combining Like Terms

Algebraic Simplification

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Pure Maths

Applied Mathematics

Logic and Functions

Decision Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.