/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 426 In the following exercises, simp... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 426

In the following exercises, simplify the given expression. $$ (12 a+4)-(9 a+6) $$

Short Answer

Expert verified
3a - 2

Step by step solution

01

Distribute the negative sign

Distribute the negative sign through the second set of parentheses to change the sign of each term inside. This results in the equation becoming: \(12a + 4 - 9a - 6\)
02

Combine like terms

Next, combine the like terms by grouping the terms with 'a' together and the constant terms together: \( (12a - 9a) + (4 - 6) \)
03

Simplify the expression

Perform the arithmetic operations inside the parentheses: \( 12a - 9a = 3a \) and \( 4 - 6 = -2 \) to get the simplified expression: \( 3a - 2 \)

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.

distributing negative signs
Let's start by understanding how to distribute negative signs. When you see a negative sign in front of parentheses, it means you need to change the sign of each term inside the parentheses. For example, in our exercise, we have:
(12a + 4) - (9a + 6).
Here, we need to distribute the negative sign to both terms inside the second parentheses. This means:
  • Change 9a to -9a
  • Change 6 to -6
So, the expression becomes:
12a + 4 - 9a - 6. This simplifies our next steps.
combining like terms
Combining like terms means to group terms that have the same variable part. In our example, after distributing the negative sign, we get:
12a + 4 - 9a - 6.
We look for terms that have the variable 'a' and the constant terms (numbers without variables).
Here, the like terms are:
  • 12a and -9a
  • 4 and -6
Combine them by adding or subtracting the coefficients (numbers in front of the variables):
(12a - 9a) + (4 - 6). This makes it easier to simplify.
simplifying expressions
The final step is simplifying the expression by performing arithmetic operations within the grouped terms. Let's simplify:
(12a - 9a) + (4 - 6).
First, handle the terms with variables:
(12a - 9a) = 3a.
Then, handle the constant terms:
(4 - 6) = -2.
So, the simplified expression is:
3a - 2. This means we have reduced the expression to its simplest form, making it easier to work with in future calculations.

One App. One Place for Learning.

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

Get started for free

Most popular questions from this chapter

In the following exercises, convert between U.S. units. Round to the nearest tenth. Naomi's baby weighed 5 pounds 14 ounces at birth. Convert the weight to ounces.

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

In the following exercises, solve using the appropriate unversions. Larry had 5 phone customer phone calls yesterday. The calls lasted \(28,44,9,75,\) and 55 minutes. How much time, in hours and minutes, did Larry spend on the(1 hour \(=60\) minutes)

In the following exercises, solve. Minh is 2 meters tall. His daughter is 88 centimeters tall. How much taller, in meters, is Minh than his daughter?

In the following exercises, evaluate each expression for the given value. If \(y=\frac{11}{12}, \quad\) evaluate: $$ (a)y+0.7+(-y) $$ $$ (b)y+(-y)+0.7 $$
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.