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Chapter 1: Problem 204

Simplify. $$ |17-8|-|13-4| $$

Short Answer

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Step by step solution

01

Evaluate the First Absolute Value

Calculate the expression inside the first absolute value: \( 17 - 8 \). This gives you \( 9 \). So, the first absolute value is \( |9| \), which is 9.
02

Evaluate the Second Absolute Value

Calculate the expression inside the second absolute value: \( 13 - 4 \). This gives you \( 9 \). So, the second absolute value is \( |9| \), which is 9.
03

Subtract the Absolute Values

Now you need to subtract the second absolute value from the first absolute value: \( 9 - 9 \). This results in 0.

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Key Concepts

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

absolute value
The absolute value of a number represents its distance from zero on the number line, without considering direction.
It鈥檚 always a positive number or zero. We denote the absolute value of the number \( x \) as \( |x| \).
For instance, \( |9| = 9 \) and \( |-9| = 9 \).
Absolute values are useful in simplifying expressions because they convert all values to positive ones.
In the exercise, we see how to handle absolute values in practical terms.
We first calculate the inside of the absolute value expressions, then apply the absolute value.
So, with \( 17 - 8 = 9 \), we get \( |9| = 9 \).
Similarly, for \( 13 - 4 = 9 \), the absolute value is \( |9| = 9 \).
simplification
Simplification is the process of reducing an expression to its simplest form.
It involves performing arithmetic operations like addition, subtraction, multiplication, and division.
In our exercise, we simplify by handling absolute values and then performing subtraction.
We start by simplifying inside the absolute value bars: \( 17 - 8 = 9 \) and \( 13 - 4 = 9 \).
After this, we take the absolute values, which remain \( 9 \) and \( 9 \).
Finally, to simplify the whole expression, we subtract these absolute values, resulting in \( 9 - 9 = 0 \).
This step-by-step approach ensures that we break down complex expressions into manageable steps.
subtraction of integers
Subtraction of integers can be thought of as adding a negative integer.
For example, \( 7 - 3 \) can be seen as \( 7 + (-3) \).
Understanding subtraction in this way helps when dealing with absolute values.
When calculating \( 17 - 8 \), we see that it鈥檚 a straightforward subtraction resulting in \( 9 \).
Similarly, calculating \( 13 - 4 \) gives us \( 9 \).
Both values are positive here and their absolute values are the same as the original values.
Finally, we subtract the second absolute value from the first: \( 9 - 9 \).
The result is \( 0 \), and this shows how integer subtraction fits into simplifying expressions with absolute values.

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