/*! 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 68 Simplify. Do not use negative ex... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 68

Simplify. Do not use negative exponents in the answer. \(3(x-7)-4(2-3 x)\)

Short Answer

Expert verified
15x - 29

Step by step solution

01

Distribute the Constants Inside the Parentheses

Apply the distributive property to the terms inside the parentheses. For the first part, multiply 3 by both terms in \( x-7 \). For the second part, multiply -4 by both terms in \( 2-3x \). \[ 3(x-7)-4(2-3x) = 3x - 21 - 8 + 12x \]
02

Combine Like Terms

Add the terms with \( x \) together and the constant terms together. \[ 3x + 12x - 21 - 8 = 15x - 29 \]

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.

simplifying expressions
Simplifying expressions involves reducing an algebraic expression to its simplest form. This often means removing parentheses and combining like terms.

First, you will distribute any numbers outside parentheses across the terms inside.

In the exercise, we use the distributive property to get:

\[ 3(x-7)-4(2-3x) = 3x - 21 - 8 + 12x \]

Next, we combine like terms to further simplify the expression.
Remember, the goal is to make the expression as simple as possible while retaining the same value.
combining like terms
Combining like terms means adding or subtracting terms that have the same variable raised to the same power.

In our example, notice the terms with the variable \( x \) are combined:
\[ 3x + 12x \]

You add these together:

\[ 3x + 12x = 15x \]

Then, the constant terms are combined by adding:

\[ -21 - 8 \]

Simplifying this gives:

\[ -21 - 8 = -29 \]

Finally, you put these results together, arriving at the simplified expression:

\[ 15x - 29 \]
algebraic expressions
An algebraic expression is a mathematical phrase that includes numbers, variables, and operational symbols like plus and minus signs.

Examples include \( 3x + 4 \) or \( 2y - 5 + z \).
These expressions can represent real-world problems and help us solve them.

The exercise given is an example of simplifying an algebraic expression.
We started with:

\[ 3(x-7)-4(2-3x) \]

Through a series of steps involving the distributive property and combining like terms, we simplified it to:

\[ 15x - 29 \]

Understanding how to work with algebraic expressions is a key skill in algebra. This helps in solving equations and understanding functions better.

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

Find the slope of the line that contains the given pair of points. a) \((5 b,-6 c),(b,-c)\) b) \((b, d),(b, d+e)\) c) \((c+f, a+d),(c-f,-a-d)\)

Without graphing, how can you tell that the graph of \(y=x-30\) passes through three quadrants?

Find the intercepts. Then graph by using the intercepts, if possible, and a third point as a check. $$ \frac{1}{3} x+\frac{1}{2} y=1 $$

Determine whether each equation is linear. Find the slope of any nonvertical lines. $$ \frac{y}{3}=x $$

Assume that \(r, p,\) and \(s\) are nonzero constants and that \(x\) and \(y\) are variables. Determine whether each equation is linear. $$ p y=s x-r^{2} y-9 $$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

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.