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Chapter 5: Problem 351

In the following exercises, translate and solve. The sum of \(n\) and \(-7.3\) is 2.4.

Short Answer

Expert verified
n = 9.7

Step by step solution

01

Translate the Problem

Translate the words into a mathematical equation. The phrase 'The sum of' indicates an addition. Therefore, 'The sum of n and -7.3' can be written as + (-7.3). The phrase 'is' indicates an equality. Therefore, we can write the equation as follows: + (-7.3) = 2.4
02

Simplify the Equation

Combine like terms in the equation. The equation simplifies to: - 7.3 = 2.4.
03

Solve for n

To isolate n, add 7.3 to both sides of the equation: - 7.3 + 7.3 = 2.4 + 7.3. This simplifies to = 9.7.
04

Verify the Solution

Substitute n = 9.7 back into the original equation to ensure it is a correct solution. + (-7.3) should equal 2.4. Therefore, 9.7 + (-7.3) = 2.4, which verifies our solution.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Translating Word Problems to Equations
Understanding how to translate word problems into equations is crucial in prealgebra. It helps you convert real-world scenarios into mathematical language.
Let's break down our example: 'The sum of \( n \) and -7.3 is 2.4.'

Here are some pointers:
  • 'The sum of' means we are adding two quantities.
  • Use \( n \) to represent an unknown number.
  • Combine \( n \) with -7.3, so write: \( n + -7.3 \).
  • 'Is' translates to an equals sign (\( = \)).
Hence, we get the equation: \( n + -7.3 = 2.4 \). This step is vital because it sets up the entire equation, making it easier for us to solve further.
Solving Linear Equations
Once you have your equation, the next step is solving it. A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable.
Our equation \( n + -7.3 = 2.4 \) is a linear equation. Follow these steps to isolate \( n \):
  • We start by simplifying the left-hand side: \( n + -7.3 \) becomes \( n - 7.3 \).
  • To isolate \( n \), we need to add 7.3 to both sides of the equation: \( n - 7.3 + 7.3 = 2.4 + 7.3 \).
  • This simplifies to \( n = 9.7 \).
Solving linear equations like this one involves careful operations to keep the equation balanced while you isolate the variable.
Verification of Solutions
After solving the equation, it's important to verify your solution. This ensures the solution is correct.

Here's how you do it for the equation \( n + -7.3 = 2.4 \):
  • We found \( n = 9.7 \).
  • Substitute 9.7 back into the original equation: \( 9.7 + -7.3 \).
  • Perform the calculation: \( 9.7 - 7.3 = 2.4 \).
  • Since both sides equal 2.4, we confirm our solution is correct.
Verification might seem like an extra step, but it's a valuable habit ensuring accuracy and understanding in problem-solving.

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