Problem 100 Simplify: \(-3(2 x-11)-4(5 x-8)\... [FREE SOLUTION]

91影视

Elementary Algebra

Laura Bracken, Ed Miller

$Math Studyset 91影视 Explanations$ Math

1 Edition

Chapter 5: Problem 100

Simplify: $-3(2 x-11)-4(5 x-8)$

Short Answer

Expert verified

-26x + 65

Step by step solution

Distribute the constants

First, distribute $-3$ through $2x - 11$ and $-4$ through $5x - 8$. This means applying the distributive property: $-3(2x - 11) = -6x + 33$ and $-4(5x - 8) = -20x + 32$.

Combine like terms

Now, combine the like terms from the results of the distribution. You have $-6x + 33$ and $-20x + 32$. Combining these, you get $-6x - 20x + 33 + 32$.

Simplify the expression

Add the like terms together. Combine the $-6x$ and $-20x$ to get $-26x$. Combine the $+33$ and $+32$ to get $+65$. Thus, the simplified expression is $-26x + 65$.

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 fundamental concept in algebra that allows us to simplify expressions. It states that you can distribute a multiplied value across terms inside a parenthesis. For example, when you have $-3(2x - 11)$, you multiply $-3$ by both $2x$ and $-11$. So, it becomes $-3 \cdot 2x - 3 \cdot (-11) = -6x + 33$. In our specific problem, we use the distributive property twice: once for $-3(2x - 11)$ and once for $-4(5x - 8)$. This gives us $-6x + 33$ and $-20x + 32$. Thoroughly applying the distributive property is the key first step to simplifying algebraic expressions.

Combining Like Terms

Combining like terms is a crucial step in simplifying algebraic expressions. Like terms are those that have the same variable raised to the same power. In the expression resulting from the distribution step $-6x + 33$ and $-20x + 32$, the $-6x$ and $-20x$ are like terms because both are terms with $x$. Similarly, $33$ and $32$ are like terms because they are constant numbers. You combine $-6x$ and $-20x$ to get $-26x$, and you combine $+33$ and $+32$ to get $+65$. Therefore, combining like terms helps simplify the expression further to a single, more manageable form.

Simplify Algebraic Expressions

Simplifying algebraic expressions involves applying various steps to make the expression as simple as possible. First, you use the distributive property to remove parentheses. Then, you combine like terms to reduce the number of terms. Through these steps, the expression becomes easier to work with and understand. In our example, we took $-3(2x - 11) - 4(5x - 8)$ and simplified it down to $-26x + 65$. Simplification makes it clear that the expression represents the same quantity but in a more streamlined and comprehensible form.

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: \(-3(2 x-11)-4(5 x-8)\)

Short Answer

Step by step solution

Distribute the constants

Combine like terms

Simplify the expression

Key Concepts

Distributive Property

Combining Like Terms

Simplify Algebraic Expressions

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Statistics

Logic and Functions

Calculus

Theoretical and Mathematical Physics

Probability and Statistics

Study anywhere. Anytime. Across all devices.