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Chapter 2: Problem 10

The difference of a number and 11 is \(-31 .\) What is the number?

Short Answer

Expert verified
The number is -20.

Step by step solution

01

Define the variable

Let the unknown number be denoted by the variable , that is, let n be the number we need to find.
02

Write the equation

According to the problem, the difference between the number n and 11 is -31. This can be written as an equation: - 11 = -31.
03

Solve the equation

To find the value of n, we need to isolate on one side of the equation. Add 11 to both sides of the equation: - 11 + 11 = -31 + 11. Simplifying this gives = -20.

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Key Concepts

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

Defining Variables
To solve any algebra problem, it helps to start by defining what you are looking for. In this exercise, we are looking to find a specific number. We don't know what this number is, so we represent it with a variable. Variables are letters or symbols used to stand in for unknown values. For example, we can call our unknown number 'n'. This step is crucial because it gives us a concrete way to work with and manipulate the unknown quantity.
Remember: Always choose a letter that makes sense to you. It could be 'x', 'y', or any other letter, but in this case, we use 'n'.
Here are some key points to note:
  • Variables are placeholders for unknown values.
  • It's easier to solve equations once you've defined your variable.
  • Clearly defining variables makes the rest of the process straightforward.
Writing Equations
Once we've defined our variable, the next step is to write an equation that represents the information given in the problem. In this exercise, we know the difference between a number (let's call it 'n') and 11 is -31. The word 'difference' suggests a subtraction operation. Therefore, we translate this information into an equation as follows: - 11 = -31.
Writing equations correctly is a critical skill in algebra. Here's what the equation tells us:
  • 'n' is our unknown number.
  • We subtract 11 from this number.
  • The result of this subtraction is -31.
Remember, equations are simply statements that two expressions are equal. In this case, the expression - 11 is equal to -31.
Solving Linear Equations
Now that we have our equation, the last step is to solve it. Solving an equation means finding the value of the unknown variable. In our example, we start with the equation: - 11 = -31. To isolate 'n', we need to get 'n' by itself on one side of the equation.
We do this by performing operations that will cancel out the other terms. Since 11 is subtracted from 'n', we add 11 to both sides of the equation to cancel it out. Our equation looks like this:
- 11 + 11 = -31 + 11.
Adding 11 to both sides simplifies the equation to:
= -20.
So, the number we are looking for is -20. Here are some key points to remember:
  • Perform the same operation on both sides of the equation to maintain the equality.
  • Simplify the equation step-by-step.
  • The goal is to isolate the variable to find its value.

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Most popular questions from this chapter

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