/*! 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 352 In the following exercises, tran... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 352

In the following exercises, translate and solve. The sum of \(n\) and \(-5.1\) is \(3.8 .\)

Short Answer

Expert verified
n = 8.9

Step by step solution

01

Translate the problem into an equation

First, we need to translate the given word problem into a mathematical equation. 'The sum of n and -5.1 is 3.8' can be written as: \[ n + (-5.1) = 3.8 \]
02

Simplify the equation

Rewrite the equation to make it easier to solve. Combine like terms: \[ n - 5.1 = 3.8 \]
03

Solve for n

To isolate the variable \( n \), add 5.1 to both sides of the equation: \[ n - 5.1 + 5.1 = 3.8 + 5.1 \] Simplify the equation: \[ n = 8.9 \]

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.

Translating Word Problems
Understanding how to translate word problems into mathematical equations is a crucial skill in solving algebraic equations. It helps to break down the problem into smaller and more manageable parts. When we translate the given problem 'The sum of n and -5.1 is 3.8', we are converting words into mathematical symbols.
The word 'sum' indicates that we are adding two numbers.
So, the phrase 'The sum of n and -5.1' translates to `n + (-5.1)`.
The word `is` typically means `=` in mathematics. Therefore, 'is 3.8' becomes `= 3.8`.
Hence, the complete equation is:





Combining Like Terms
Once we have translated the word problem into an equation, the next step is to simplify it by combining like terms. Like terms are terms in an equation that have the same variable raised to the same power. In our equation
`n + (-5.1) = 3.8`, we can simplify it by recognizing that adding a negative number is the same as subtraction.
This gives us:
`n - 5.1 = 3.8`.
Now, the equation is simpler, with `n` as the variable term and `-5.1` as the constant term on the left side and `3.8` as the constant term on the right side.
Isolating the Variable
The final step in solving an equation is to isolate the variable on one side of the equation. In our simplified equation `n - 5.1 = 3.8`, we need to get `n` by itself.
To do this, we perform the inverse operation on both sides. Since `5.1` is being subtracted from `n`, we add `5.1` to both sides to cancel it out:

`n - 5.1 + 5.1 = 3.8 + 5.1`

This simplifies to:
`n = 8.9`.

Now, `n` is isolated, and we've found that `n` equals `8.9`.
Remember, isolating the variable is about performing the same operation on both sides of the equation to keep it balanced.
By doing this, we can solve for the unknown variable efficiently.

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

In the following exercises, find each unit price and then identify the better buy. Round to three decimal places. Toothpaste, 6 ounce size for \(\$ 3.19\) or 7.8 -ounce size for \(\$ 5.19\)

In the following exercises, locate each number on a number line. $$0.8$$

In the following exercises, find the unit rate. Round to two decimal places, if necessary. The pressroom at a printing plant prints 540,000 sections in 12 hours. How many sections are printed per hour?

In the following exercises, translate the English phrase into an algebraic expression. 105 calories in \(x\) ounces

The average American produces about \(1,600\) pounds of paper trash per year \((365\) days. How many pounds of paper trash does the average American produce each day? (Round to the nearest tenth of a pound.)
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Discrete 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.