/*! 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 367 In the following exercises, simp... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 367

In the following exercises, simplify. $$ 9(6 x-11)+15 $$

Short Answer

Expert verified
Simplified expression: \(54x - 84\).

Step by step solution

01

- Distribute the 9

Multiply each term inside the parentheses by 9. This means calculating both \(9 \times 6x\) and \(9 \times -11\).
02

- Calculate the products

First, \(9 \times 6x = 54x\). Next, \(9 \times -11 = -99\). So, the expression becomes \(54x - 99 + 15\).
03

- Combine like terms

Combine the constant terms \(-99 + 15\). This simplifies to \(-84\). The expression now is \(54x - 84\).

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.

distribution in algebra
Distribution in algebra is a very important concept. When you see an expression like \(9(6x-11)\), you need to use the distributive property to simplify it. This property helps spread the multiplication over addition or subtraction inside the parentheses.
The distributive property is defined as: \(a(b + c) = ab + ac\).
So in our example, we multiply 9 by each term inside the parentheses: \(9 \times 6x\) and \(9 \times -11\).
Here鈥檚 how you do it step-by-step:
  • First, multiply 9 by 6x, which is \(54x\).
  • Then, multiply 9 by -11, which is \(-99\).
Now, our expression looks like this: \(54x - 99\).
Simple, right? Always remember to distribute the outer number to every term inside the parentheses to break them down.
combining like terms
Combining like terms is the next key concept. Like terms are terms that have the same variable raised to the same power.
Look at our expression from the previous step: \(54x - 99 + 15\). We have:
  • One term with \(x\) which is \(54x\)
  • Two constant numbers, -99 and 15
When combining like terms, we group the constants together:
First, we calculate \(-99 + 15\). This gives us \(-84\).
Now, our expression simplifies to \(54x - 84\).
Combining like terms helps in making the expression simpler and easier to read.
simplification steps
Let's look at the full simplification process again.
We started with the expression \(9(6x - 11) + 15\).
  • Step 1: Distribute the 9 to both terms inside the parentheses:
    \(9 \times 6x = 54x\) and \(9 \times -11 = -99\)
  • Step 2: Rewrite the expression as \(54x - 99 + 15\)
  • Step 3: Combine the constants \(-99 + 15\), to get -84.
The final simplified expression is \(54x - 84\).
Follow these simplification steps, and you鈥檒l easily master algebraic expressions. Note that simplifying expressions makes solving equations faster and more efficient.

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, simplify. $$ \frac{2}{3} \cdot 28 \cdot \frac{3}{7} $$

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

In the following exercises, simplify using the commutative and associative properties. $$ (3.98 d+0.75 d)+1.25 d $$

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, identify whether each example is using the identity of addition or multiplication. $$ 29+0=29 $$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Decision 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.