/*! 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 55 In Problems 49-58, find the valu... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 55

In Problems 49-58, find the value of each expression if \(x=3\) and \(y=-2\). \(|4 x-5 y|\)

Short Answer

Expert verified
The value is 22.

Step by step solution

01

- Substitute the values

Substitute the given values of \(x = 3\) and \(y = -2\) into the expression \(4x - 5y\).
02

- Perform the multiplication

Calculate the value of \(4x\) and \(-5y\).\[4x = 4 \cdot 3 = 12\]\[-5y = -5 \cdot (-2) = 10\]
03

- Add the results

Sum the results from Step 2:\[4x - 5y = 12 + 10 = 22\]
04

- Apply the absolute value

Find the absolute value of the result from Step 3:\[|22| = 22\]

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.

Absolute Value
Absolute value tells us how far a number is from zero on the number line. It is always non-negative. For example, the absolute value of both 22 and -22 is 22, because both are 22 units away from zero. We use vertical bars to show absolute value: \(|a|\). In our exercise, even though the result of the expression \(4x - 5y\) was 22, we took the absolute value which still remains 22, as 22 is already a positive number.
Substitution
Substitution means replacing variables in an expression with their given values. In this exercise, we were given \(x = 3\) and \(y = -2\). So, we substituted these values into the expression \(4x - 5y\). Substituting helps in simplifying the expression to find the actual numerical value. For example, the expression \(4x\) turned into \(4 \cdot 3\).
Algebraic Expressions
An algebraic expression includes numbers, variables, and operators (like +, -, *, /). In our problem, \(4x - 5y\) is an algebraic expression as it combines constants, variables, and the operations of multiplication and subtraction. Understanding how to handle each component correctly is crucial for simplification and finding the final value.
Multiplication and Addition
First, we need to multiply each term independently. In the given exercise, we calculated \(4x\) by multiplying 4 and 3 to get 12. Similarly, for \(-5y\), multiplying \(-5\) by \(-2\) gives us 10. Remember, multiplying two negatives makes a positive. Finally, we added the results of the multiplications. Adding 12 and 10 gave us 22. Multiplication and then addition follow the order of operations: PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

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

Rationalize the denominator of each expression. Assume that all variables are positive when they appear. $$\frac{\sqrt{3}-1}{2 \sqrt{3}+3}$$

Expressions that occur in calculus are given. Factor each expression. Express your answer so that only positive exponents occur. $$2 x(3 x+4)^{4 / 3}+x^{2} \cdot 4(3 x+4)^{1 / 3}$$

Expressions that occur in calculus are given. Factor each expression. Express your answer so that only positive exponents occur. (x+1)^{3 / 2}+x \cdot \frac{3}{2}(x+1)^{1 / 2} \quad x \geq-1

Rationalize the denominator of each expression. Assume that all variables are positive when they appear. $$\frac{-\sqrt{3}}{\sqrt{8}}$$

Simplify each expression. $$(-1000)^{-1 / 3}$$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Pure Maths

Read Explanation

Mechanics 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.