/*! 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 26 Subtract \(23 x-5 y\) from the s... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 26

Subtract \(23 x-5 y\) from the sum of \(6 x+15 y\) and \(x-19 y\)

Short Answer

Expert verified
The result of the operation is \(-16x + y\).

Step by step solution

01

Perform the Sum

First, add together the expressions \(6 x+15 y\) and \(x-19 y\). This is done by combining like terms (terms that are multiples of the same variable). So, add the x terms (\(6x + x\) which equals \(7x\)) and the y terms (\(15y - 19y\) which equals \(-4y\)). Combining these gives the sum \(7x - 4y\)
02

Perform the Subtraction

Next, subtract the expression \(23x - 5y\) from the sum obtained in the previous step. It's important to remember that subtracting an expression is equivalent to adding its negative. Therefore, subtract \(23x\) and \(-5y\) separately from the sum. This gives \(7x - 23x\) which equals \(-16x\) and \(-4y - (-5y)\) which equals \(y\). Thus, combining these gives the result \(-16x + y\).

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 algebra that makes expressions simpler and easier to work with. When you have terms in an expression that include the same variable raised to the same power, these are called "like terms."
For example, in an expression like \(6x + x\), both terms contain the variable \(x\) raised to the first power, making them like terms. You simply add or subtract the coefficients (the numbers in front of the variables). So, \(6x + x = 7x\).
Similarly, the terms \(15y - 19y\) combine to \(-4y\) by subtracting 19 from 15.

Here are some quick tips:
  • Identify terms with the same variables and powers 鈥� these are your like terms.
  • Add or subtract coefficients while keeping the variable part unchanged.
  • Be mindful of negative signs as they affect both the sign and the value of the coefficient.
Polynomial Operations
Polynomial operations typically involve adding, subtracting, and sometimes multiplying or dividing expressions that are made up of variables and constants. In this exercise, we focus on addition and subtraction of polynomials.
When adding polynomials like \((6x + 15y) + (x - 19y)\), you first group and combine like terms:
  • Add \(6x\) and \(x\) to get \(7x\).
  • Add \(15y\) and \(-19y\) to get \(-4y\).
This results in a new polynomial \(7x - 4y\).

Polynomial operations are key to simplifying expressions and solving equations. They involve techniques that help:
  • Simplify complicated expressions into more manageable forms.
  • Set the stage for solving algebraic equations effectively.
  • Enable further mathematical operations, such as factoring or expanding.
Subtraction of Expressions
Subtracting algebraic expressions involves careful handling of each term, particularly because subtraction is not as straightforward as addition. You often have to think of subtraction as "adding the negative" of the second expression.
For instance, to subtract \(23x - 5y\) from \(7x - 4y\), you rewrite the subtraction as adding a negative:
  • This becomes \(7x - 4y - (23x - 5y)\) which simplifies to \(7x - 4y + (-23x + 5y)\).
  • Distribute the negative sign across the second expression.
  • Combine like terms: \(7x - 23x = -16x\) and \(-4y + 5y = y\).
This results in the expression \(-16x + y\).

Subtraction in algebra is key because:
  • It requires attention to detail as each term's sign affects the outcome.
  • Helps to explore and simplify further algebraic processes.
  • Supports the development of core mathematical problem-solving skills.

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

perform the indicated operations. $$\begin{aligned} &\left[\left(7 y^{2}-4 y+2\right)-\left(12 y^{2}+3 y-5\right)\right]-\left[\left(5 y^{2}-2 y-8\right)+\left(-7 y^{2}+10 y-13\right)\right] \end{aligned}$$

In Exercises \(156-163\), determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$\left(7 \times 10^{5}\right)+\left(2 \times 10^{-3}\right)=9 \times 10^{2}$$

Will help you prepare for the material covered in the next section. $$\text { Simplify: } \frac{\left(x^{2}\right)^{3}}{5^{3}}$$

determine whether each statement 鈥渕akes sense鈥� or 鈥渄oes not make sense鈥� and explain your reasoning. As long as I understand how to add and subtract polynomials, I can select the format, horizontal or vertical, that works best for me.

Subtract \(x^{3}-2 x^{2}+2\) from the sum of \(4 x^{3}+x^{2}\) and \(-x^{3}+7 x-3\)
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

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.