/*! 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 76 Simplify each expression. $$ ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 76

Simplify each expression. $$ -2(3 r-4)-(6-r)+2 r-5 $$

Short Answer

Expert verified
-3r - 3

Step by step solution

01

Distribute the multiplication

Distribute -2 with (3r - 4): -2 * 3r + (-2) * (-4) This simplifies to: -6r + 8 The expression is now: -6r + 8 - (6 - r) + 2r -5
02

Distribute the negative sign in the parentheses

Distribute the -1 to each term in the parentheses: - (6 - r): - 6 + r The expression is now: -6r + 8 - 6 + r + 2r - 5
03

Combine like terms

Combine the terms with r and the constant terms separately: -6r + r + 2r = -3r And: 8 - 6 - 5 = -3 So, the simplified expression is: -3r - 3

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 useful algebraic property that allows us to multiply a single term across terms inside parentheses. This property is stated mathematically as: \[ a(b + c) = ab + ac \] In our problem, we used the distributive property to multiply -2 with (3r - 4). Here's the process: - Multiply -2 by 3r: \( -2 * 3r = -6r \)
- Multiply -2 by -4: \( -2 * -4 = 8 \)
After distribution, we get: \( -6r + 8 \)
Keep in mind that the distributive property works both ways. We use it to simplify expressions and solve equations efficiently.
Combining Like Terms
Once you've used the distributive property, the next step is to combine like terms. Like terms are terms that have the same variable raised to the same power. Here鈥檚 how we combined the like terms:
- First, list all terms with the variable r: \( -6r + r + 2r \)
- Add them together: \( -6r + r + 2r = -3r \)
- Next, combine the constant terms: \( 8 - 6 - 5 \)
This simplifies to: \( 8 - 6 = 2 \), and then \( 2 - 5 = -3 \)
Combining like terms helps us to reduce the expression to a simpler form. Always remember to keep track of the signs and coefficients.
Negative Signs in Algebra
Negative signs can be tricky in algebra, but understanding how to handle them is key. Let's see how they affect our operations:
- When distributing a negative sign, it reverses the sign of each term inside the parentheses. In our problem: \( -(6 - r) \)
鈥� Distribute -1 to each term: \( -1 * 6 = -6 \)
\( -1 * -r = r \)
This results in: \( -6 + r \)
- Negative signs also play a role when combining terms. Be careful with subtraction and adding negative numbers. Properly managing negative signs ensures accuracy in your work.

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

Evaluate each expression for \(x=6, y=-4,\) and \(a=3\) $$ (2 x+y)(3 a) $$

Evaluate each expression for \(x=6, y=-4,\) and \(a=3\) $$ \frac{2 y^{2}-x}{a+10} $$

Write each sentence as an equation, using \(x\) as the variable. Then find the solution from the set of integers between \(-12\) and \(12,\) inclusive. 6 less than a number is 4

To find the average (mean) of numbers, we add the numbers and then divide the sum by the number of terms added. For example, to find the average of \(14,8,3,9,\) and \(1,\) we add them and then divide by 5. $$ \frac{14+8+3+9+1}{5}=\frac{35}{5}=7 \leftarrow \text { Average } $$ Find the average of each group of numbers. $$ -15,29,8,-6 $$

Translate each phrase into a mathematical expression. Use \(x\) as the variable. Combine like terms when possible. Six times a number added to \(-4,\) subtracted from twice the sum of three times the number and 4 (Hint: Twice means two times.)
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

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.