Problem 69 Simplify each expression. $$ ... [FREE SOLUTION]

91影视

Chapter 1: Problem 69

Simplify each expression. $$ a-(4 a-1) $$

Short Answer

Expert verified

-3a + 1

Step by step solution

Distribute the negative sign

The expression is given as a - (4a - 1) Distribute the negative sign inside the parentheses: a - 4a + 1

Combine like terms

Combine the terms that have 'a': a - 4a = -3a. The simplified expression is: -3a + 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

To simplify algebraic expressions, we often use the distributive property. This property helps us distribute (or spread out) multiplication over addition or subtraction inside parentheses. In the expression given in the exercise, we have a negative sign outside the parentheses:

$ a - (4a - 1) $

By applying the distributive property, we distribute the negative sign to both terms inside the parentheses. This means we multiply both $4a$ and $-1$ by $-1$. Here, it looks like this:

\[ a - 4a + 1 \]

Notice how the negative sign changes the sign of each term inside the parentheses. Distributing like this makes combining the terms much more straightforward!

Combining Like Terms

After using the distributive property, you鈥檙e left with:

\[ a - 4a + 1 \]

Combining like terms is our next step. 'Like terms' are terms whose variables and their exponents match. Here, both $a$ and $- 4a$ are like terms because they both contain the variable $a$.

To combine them, simply perform the operations with their coefficients (the numbers in front of the variables). So:

\[ a - 4a = - 3a \]

This combining results in $- 3a$. Don't forget to bring down the constant term $+1$, which leaves us with:

\[- 3a + 1 \]

You now have a simplified algebraic expression.

Negative Sign Distribution

Let's delve deeper into the negative sign distribution. The negative sign (or subtraction) changes both the sign and the value of each term within the parentheses.

For example, with \[ a - (4a - 1) \], distributing the negative sign makes it look like:

\[ a - 4a + 1 \]

Think of it as multiplying $4a - 1 $ by $-1$.

Here鈥檚 a key point:

When distributing $-1 $ to $+4a $, it becomes \- 4a
When distributing $-1$ to $-1$, it turns into $+1 $

This step ensures that every term inside the parentheses is correctly adjusted by the negative sign. Making sure this is done correctly is crucial to simplify the expression accurately.

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. $$ a-(4 a-1) $$

Short Answer

Step by step solution

Distribute the negative sign

Combine like terms

Key Concepts

Distributive Property

Combining Like Terms

Negative Sign Distribution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Mechanics Maths

Decision Maths

Probability and Statistics

Calculus

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.