/*! 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 80 Combine like terms. \(-7+10.5 ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 80

Combine like terms. \(-7+10.5 y+13+(-11.5 y)\)

Short Answer

Expert verified
6 - 1.0y

Step by step solution

01

Identify Like Terms

Look at the given expression equation equals -7 + 10.5 y + 13 + (-11.5 y). The like terms are the constants and the terms containing the variable y. The constants are -7 and 13. The terms containing the variable y are 10.5y and -11.5y.
02

Combine Constant Terms

Add the constant terms together: equation -7 + 13. which is equal to: -7 + 13 = 6_eq.
03

Combine Variable Terms

Next, add the terms containing the variable y: equation 10.5 y + (-11.5 y),which simplifies to: 10.5y - 11.5y = -1.0y.
04

Write the Final Expression

Put the combined like terms together to form the final simplified expression: equation 6 - 1.0y.

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.

algebraic expressions
Algebraic expressions consist of constants, coefficients, and variables combined using operations like addition, subtraction, multiplication, and division. Constants are fixed numbers, while coefficients are numbers that multiply variables. Variables, represented by letters like \(x\), \(y\), or \(z\), can change values.
For example, in the expression \(-7 + 10.5y + 13 - 11.5y\), -7 and 13 are constants, while 10.5 and -11.5 are coefficients of the variable \(y\).
Understanding these basic components is crucial for simplifying and manipulating algebraic expressions effectively.
simplifying expressions
Simplifying expressions means making them easier to work with by reducing them to their simplest form.
This involves combining like terms, which are terms that have the same variable raised to the same power.
In the example \(-7 + 10.5y + 13 - 11.5y\), we have like terms \(-7\) and \(13\), which are constants, and like terms \(10.5y\) and \(-11.5y\), which have the variable \(y\).
Combining these like terms simplifies the expression to its simplest form, making further calculations more straightforward.
combining variables
Combining variables is a key step in simplifying algebraic expressions.
It involves adding or subtracting terms that share the same variable.
For example, in the expression \(10.5y - 11.5y\), both terms contain the variable \(y\).
To combine these, subtract the coefficients: \(10.5 - 11.5 = -1\). So, \(10.5y - 11.5y\) simplifies to \(-1.0y\).
This reduced form makes it easier to handle and understand the expression, ultimately simplifying the problem-solving process.
Remember, only terms with the exact same variable and exponent can be combined in this way.

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

SYNTHESIS Write the sentence \((-x)^{2} \neq-x^{2}\) in words. Explain why \((-x)^{2}\) and \(-x^{2}\) are not equivalent.

Write a true sentence using either \(<,>,\) or \(=\). $$|-5| \square|-2|$$

Simplify. $$ 12 a^{2}-3 a b+5 b^{2}-5\left(-5 a^{2}+4 a b-6 b^{2}\right) $$

Simplify. $$ 5 t^{3}+t+3\left(t-2 t^{3}\right) $$

Given that \(0.3 \overline{3}=\frac{1}{3}\) and \(0.6 \overline{6}=\frac{2}{3},\) express each of the following as a ratio of two integers. $$7.7 \overline{7}$$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

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.