/*! 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 8 Simplify by clearing parentheses... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 8

Simplify by clearing parentheses and combining like terms. $$-6.9 y+4.23 y$$

Short Answer

Expert verified
-2.67y

Step by step solution

01

Identify the Like Terms

Look at the terms given in the expression \(-6.9y\text{ and }4.23y\). Both terms have the variable \(y\), so they are like terms.
02

Combine the Like Terms

To combine the like terms, add the coefficients together. Perform the arithmetic operation: \(-6.9 + 4.23 = -2.67\).
03

Write the Simplified Expression

Attach the combined coefficient to the common variable \(y\). Therefore, the simplified expression is \(-2.67y\).

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.

Combining Like Terms
Combining like terms is a fundamental skill in simplifying algebraic expressions. In algebra, 'like terms' are terms that have the same variables raised to the same power. For instance, in the expression \(-6.9y + 4.23y\), the terms \(-6.9y\) and \(4.23y\) are 'like terms' as they both contain the variable \(y\).
To combine these, you'll just add their coefficients (the numerical part of the terms). Here, you perform the operation: \(-6.9 + 4.23 = -2.67\).
Then, attach the resulting coefficient to the common variable, leading to \(-2.67y\).
This process is crucial as it simplifies expressions, making them easier to work with in further calculations.
Algebraic Expressions
An algebraic expression is a mathematical phrase that can include numbers, variables, and operation symbols (such as +, -, \(\times\), \( \div\)).
Expressions can be simple, like \(4y\), or complex, like \(-6.9y+4.23y\). The key is understanding what each part represents.
Here are some common components:
  • **Variables:** Symbols, often letters, which represent unknown values (e.g., \(y\)).
  • **Coefficients:** Numbers multiplying the variables (e.g., \(-6.9\) in \(-6.9y\)).
  • **Constants:** Standalone numbers without variables (none in this exercise).
In simplifying these expressions, we often combine like terms and perform arithmetic operations on the coefficients, just like in the given exercise.
Coefficients
A coefficient is the numerical part of a term that includes a variable.
For example, in \(-6.9y\), -6.9 is the coefficient.
Coefficients can be positive, negative, integers, or decimals.
They are crucial because they quantify the variable. In the given exercise, the coefficients were -6.9 and 4.23 for the terms \(-6.9y\) and \(4.23y\).
When simplifying, you focus on adding or subtracting these coefficients.

Here's a brief recap of what we did:
  • Identified the like terms \(-6.9y \text{ and } 4.23y\)
  • Added the coefficients \(-6.9 + 4.23 = -2.67\)
  • Attached the resulting coefficient to the variable \(y\)
This gave us the simplified term \(-2.67y\). It's a systematic process once you understand each component!

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

For Exercises \(59-66,\) simplify the expressions. $$(-1.3)^{2}$$

A cell phone plan has a \(\$ 39.95\) monthly fee and includes 450 min. For time on the phone over 450 min, the charge is \(\$ 0.40\) per minute. How much is Jorge charged for a month in which he talks for 597 min?

Evaluate the expression for the given value(s) of the variables Use 3.14 for \(\pi\). $$-\frac{1}{2} g t^{2} \text { for } g=9.8 \text { and } t=4$$

Olivia's diet allows her 60 grams (g) of fat per day. If she has \(\frac{1}{4}\) of her total fat grams for breakfast and a McDonald's Quarter Pounder \((20.7\) g of fat) for lunch, how many grams does she have left for dinner?

A hotel gift shop ordered 40 T-shirts at \(\$ 8.69\) each, 10 hats at \(\$ 3.95\) each, and 20 beach towels at \(\$ 4.99\) each. What was the total cost of the merchandise, including the \(\$ 29.21\) sales \(\operatorname{tax} ?\)
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

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.