/*! 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 88 Simplify each expression. See Se... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 88

Simplify each expression. See Section \(1.8 .\) \(8(z-6)+7 z-1\)

Short Answer

Expert verified
The simplified expression is \(15z - 49\).

Step by step solution

01

Distribute the Coefficient

First, apply the distributive property to the expression: \[ 8(z-6) \]This means multiplying 8 with each term inside the parentheses. \[ 8(z) - 8(6) = 8z - 48 \]So, the expression becomes: \[ 8z - 48 + 7z - 1 \]
02

Combine Like Terms

Now, identify and combine the like terms from the expression. We have two like terms that involve \(z\):\[ 8z + 7z \]Combine them:\[ 15z \]Similarly, combine the constant terms:\[ -48 - 1 \]Simplifying this gives:\[ -49 \]Now the expression is:\[ 15z - 49 \]

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 rule that helps us simplify expressions by allowing us to multiply a single term by each term within a set of parentheses. Consider the expression \(8(z - 6)\). Here, we're using the distributive property.

This signifies that we will multiply 8 with both \(z\) and \(-6\). Let's break it down further:
  • First, multiply \(8\) by \(z\), resulting in \(8z\).
  • Then, multiply \(8\) by \(-6\), giving us \(-48\).
So, distributing \(8\) through the parentheses transforms it to \(8z - 48\).

Distributive property is quite handy, especially when dealing with expressions that involve parentheses, because it allows you to simplify the terms and eventually makes solving equations easier.
Combining Like Terms
After using the distributive property, the expression might still have several terms that can be made even simpler. This involves combining like terms. Like terms are terms that have the same variable part. In the expression \(8z - 48 + 7z - 1\), let's identify them:
  • The terms \(8z\) and \(7z\) are like terms because they both have \(z\).
  • The constants \(-48\) and \(-1\) are also like terms because they don't have any variables associated with them.
Combine \(8z\) and \(7z\) to get \(15z\). For the constant terms \(-48\) and \(-1\), adding them gives \(-49\).

Combining like terms is essentially addition and subtraction of the coefficients of these terms, which makes the expression more refined and easier to work with.
Simplification
Simplification is the final stage in refining an algebraic expression to its simplest form. After distributing and combining like terms, as shown earlier, we're left with \(15z - 49\). Let's take a closer look at this process:
  • Simplification means ensuring there are no more like terms left to be combined.
  • It also checks that there's minimal redundancy in the expression.
In cases like \(15z - 49\), this is as simple as it can get because:
  • There are no more like terms to combine.
  • The expression doesn't have any factors that can be simplified further without changing its value.
Simplification not only makes the expression more elegant but also easier to interpret and use in further calculations or real-world applications.

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

Solve. For Exercises 1 through \(4,\) write each of the following as equations. The sum of twice a number and 7 is equal to the sum of the number and 6 . Find the number.

During the 2009 Rose Bowl, University of Southern California beat Pennsylvania State University by 14 points. If their combined scores totaled \(62,\) find the individual team scores.

The area of the Sahara Desert is 7 times the area of the Gobi Desert. If the sum of their areas is 4,000,000 square miles, find the area of each desert.

Solve. For Exercises 1 through \(4,\) write each of the following as equations. The sum of 4 times a number and -2 is equal to the sum of 5 times the number and \(-2 .\) Find the number.

Dr. Dorothy Smith gave the students in her geometry class at the University of New Orleans the following question. Is it possible to construct a triangle such that the second angle of the triangle has a measure that is twice the measure of the first angle and the measure of the third angle is 5 times the measure of the first? If so, find the measure of each angle. (Hint: Recall that the sum of the measures of the angles of a triangle is \(180^{\circ} .\) )
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Geometry

Read Explanation

Logic and Functions

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.