/*! 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 44 Evaluate each expression if \(x=... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 44

Evaluate each expression if \(x=-2\) and \(y=3\). \(-2 x+x y\)

Short Answer

Expert verified
-2

Step by step solution

01

Identify and Substitute Values

First, identify the given values for the variables. Here, we are given that \(x=-2\) and \(y=3\). Now, substitute these values into the expression \(-2x + xy\).
02

Substitute and Simplify

Substitute \(x = -2\) and \(y = 3\) into the expression:\[-2(-2) + (-2)(3)\]
03

Evaluate the Multiplications

Evaluate the multiplications separately:\(-2(-2) = 4\)and\(-2)(3) = -6\)
04

Add the Results

Combine the results from Step 3:\[4 + (-6) = 4 - 6 = -2\]

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.

Variable substitution
Variable substitution is an essential process in algebra that helps you simplify and solve expressions. You start by identifying the given values of the variables.
In our exercise, we have two variables: \(x\) and \(y\). We know that \(x = -2\) and \(y = 3\), so we replace these variables with their values in the expression. The original expression is \(-2x + xy\).
By substituting \(x = -2\) and \(y = 3\), we transform the expression into:
\[-2(-2) + (-2)(3)\]
This substitution allows us to move forward with evaluating the expression.
Expression simplification
Once variables are substituted, the next step is to simplify the expression.
For our exercise, after substituting \(x = -2\) and \(y = 3\), we get:
\[-2(-2) + (-2)(3)\]
Simplification involves making the expression easier to understand and solve. Here, we'll resolve the individual multiplications before combining the results.
This transforms complex expressions into a simpler, more manageable form.
Multiplication in algebra
Multiplication in algebra is just like basic arithmetic but with variables. Here鈥檚 how it works in our example:
We have the products \(-2(-2)\) and \((-2)(3)\).
  • First, \(-2\) times \(-2\): Two negatives make a positive, so \(-2 \times -2 = 4\).
  • Next, \(-2\) times \(3\): A negative times a positive gives a negative, so \(-2 \times 3 = -6\).

Understanding these rules of multiplication helps you easily evaluate each part of the expression.
Addition and subtraction in algebra
Finally, we need to perform addition and subtraction to combine our results.
From our multiplication steps, we have the numbers \(4\) and \(-6\).
To combine them, you proceed with addition and subtraction:
\[4 + (-6)\]
Adding a negative number is the same as subtracting its absolute value, so:
\[4 + (-6) = 4 - 6 = -2\]
This final result is the value of the original expression after evaluating all components.

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

Expressions that occur in calculus are given. Write each expression as a single quotient in which only positive exponents and radicals appear. $$2 x\left(x^{2}+1\right)^{1 / 2}+x^{2} \cdot \frac{1}{2}\left(x^{2}+1\right)^{-1 / 2} \cdot 2 x$$

Use a calculator to approximate each radical. Round your answer to two decimal places. $$\frac{2+\sqrt{3}}{3-\sqrt{5}}$$

Simplify each expression. $$\left(-\frac{64}{125}\right)^{-2 / 3}$$

Rationalize the denominator of each expression. Assume that all variables are positive when they appear. $$\frac{1}{\sqrt{2}}$$

Simplify each expression. $$\left(\frac{27}{8}\right)^{2 / 3}$$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Geometry

Read Explanation

Pure Maths

Read Explanation

Calculus

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.