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Chapter 2: Problem 58

Evaluate \(x-y\) for the given replacement values. $$ x=9 \text { and } y=-2 $$

Short Answer

Expert verified
The result is 11.

Step by step solution

01

Substitute the Values

Substitute the given values into the expression. Here, replace \(x\) with 9 and \(y\) with -2 in the equation \(x - y\).
02

Simplify the Expression

Simplify the expression by calculating \(9 - (-2)\). This can be rewritten as \(9 + 2\) since subtracting a negative number is the same as adding its positive.
03

Perform the Calculation

Perform the computation \(9 + 2\) which gives the result \(11\).

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Key Concepts

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

Substitute Values
Substituting values is like filling in the gaps in a puzzle. Imagine you have an expression with unknowns (like the pieces of the puzzle), and you want to know what it equals when each of these unknowns is given specific numbers. In the expression \(x - y\), if we know that \(x = 9\) and \(y = -2\), we simply replace \(x\) with 9 and \(y\) with -2.
This is how substitution works:
  • Start with your expression: \(x - y\).
  • Replace the variable \(x\) with the value 9.
  • Replace the variable \(y\) with the value \(-2\).
Now the expression looks like this: \(9 - (-2)\). Substitution is a powerful tool in mathematics that allows you to evaluate expressions by using given numbers, making the problem easier to solve.
Simplification
Once you substitute values into an expression, the next step is to simplify it. Simplifying means making the expression as easy to understand as possible. With our expression \(9 - (-2)\), there is an interesting twist: subtracting a negative number.
When you subtract a negative, it's similar to adding the positive version of that number. So:
  • \(9 - (-2) = 9 + 2\).
  • This turns a potentially confusing situation into a straightforward addition problem.
Simplification also involves performing basic operations like addition and subtraction to condense the expression to a simpler form, preparing it for the final calculation. It's like cleaning up your workspace so you're ready to tackle the main task without obstacles.
Negative Numbers
Negative numbers can be tricky, especially when combined with subtraction. Understanding how negative numbers work is essential for correctly evaluating expressions. Let's take a closer look:
  • Negative numbers are like temperatures below zero, they have 'cold' values.
  • When you subtract a negative number, imagine you are removing the coldness, which actually warms things up or increases the value.
    • In our example, when we subtract \(-2\) from 9, we are effectively adding 2:
    • \(9 - (-2)\) becomes \(9 + 2\).
    Understanding negative numbers helps to avoid mistakes and makes solving math problems more intuitive. They teach us that subtraction can sometimes be about addition, depending on the numbers involved.

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