/*! 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 60 Evaluate \(x+y\) for the given r... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 60

Evaluate \(x+y\) for the given replacement values. $$ x=-1 \text { and } y=-29 $$

Short Answer

Expert verified
The value of \(x+y\) is \(-30\).

Step by step solution

01

Understand the Problem

We need to find the sum of two variables, \(x\) and \(y\). The given values for the variables are \(x = -1\) and \(y = -29\).
02

Substitute the Given Values

Replace \(x\) with \(-1\) and \(y\) with \(-29\) in the expression \(x + y\).
03

Perform the Addition

Calculate the sum by adding the substituted values: \(-1 + (-29)\). Combine the numbers: \(-1 - 29 = -30\).
04

Interpret the Result

The result of the addition gives us the value of \(x + y\). In this case, \(x + y = -30\).

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 a fundamental concept in algebra where we replace variables in an expression with specific values. In this exercise, we are given the variables \( x \) and \( y \) with the values -1 and -29, respectively. The process is simple: You look at an algebraic expression, like \( x + y \), and then simply swap each variable with its given number.
  • For \( x + y \), wherever you see \( x \), substitute it with -1.
  • Similarly, wherever you find \( y \), substitute it with -29.
After substitution, our expression changes from \( x + y \) to \(-1 + (-29)\). This allows us to evaluate the expression using basic arithmetic next.
Negative Numbers
Understanding negative numbers is crucial when dealing with integer addition, especially when both numbers are negative. In our example, both values, -1 and -29, are negative.
Negative numbers lie to the left of zero on the number line. When you add two negative numbers together, the result is more negative than either number individually. Think of adding negative numbers as moving farther left on the number line.
So, when adding \(-1\) and \(-29\):
  • You begin at -1 and move 29 more steps to the left.
  • This leads you to -30, which can be thought of as -1 flattened and reinforced by -29 more units.
Being comfortable with negative numbers helps in understanding why \(-1 + (-29)\) simplifies to \(-30\).
Basic Arithmetic
Basic arithmetic is used to calculate the result after substituting the variables. When both numbers in an addition operation are negative, you add them just as you would positive numbers, but keep the negative sign.
Here's a breakdown:
  • Start by aligning the absolute values (ignoring signs): 1 and 29.
  • Add these numbers as usual: \(1 + 29 = 30\).
  • Finally, since both original numbers were negative, keep the result negative: \(-30\).
So, the final result after the arithmetic operation with these negative inputs is \(-30\). This simple method helps reduce confusion when adding negative numbers, ensuring accuracy in calculating sums involving negatives.

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

Answer true or false. Zero is always less than a positive number.

Evaluate: \(\quad-(-|-8|)\)

Write the given numbers in order from least to greatest. $$ 1^{4},-(-3),-|7|,|-20| $$

Represent each quantity by an integer. A scuba diver is swimming 25 feet below the surface of the water in the Gulf of Mexico.

Represent each quantity by an integer. The lowest elevation in the United States is found at Death Valley, California, at an elevation of 282 feet below sea level.
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

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.