To solve the expression \(\frac{|2r - s|}{5t + 10}\), follow these steps:
1. Calculate the numerator:
- The numerator is the absolute value of \(2r - s\), represented as \(|2r - s|\).
- Evaluate \(2r - s\).
- Take the absolute value of this result.
2. Calculate the denominator:
- The denominator is \(5t + 10\).
- Evaluate \(5t + 10\).
3. Divide the numerator by the denominator:
- Take the absolute value result from step 1 and divide it by the result of step 2.
Let's break this down with an example:
### Example:
Given \(r = 3\), \(s = 7\), and \(t = -2\):
1. Calculate the numerator:
- Evaluate \(2r - s\):
[tex]\[
2 \cdot 3 - 7 = 6 - 7 = -1
\][/tex]
- Take the absolute value of this result:
[tex]\[
|-1| = 1
\][/tex]
2. Calculate the denominator:
- Evaluate \(5t + 10\):
[tex]\[
5 \cdot -2 + 10 = -10 + 10 = 0
\][/tex]
3. Divide the numerator by the denominator:
- This gives:
[tex]\[
\frac{1}{0}
\][/tex]
Since the denominator is 0, the expression is undefined (division by zero is not possible).
### General Case:
For any values of \(r\), \(s\), and \(t\):
1. Calculate the numerator:
- \(2r - s\)
- Then \(|2r - s|\)
2. Calculate the denominator:
- \(5t + 10\)
3. Divide these two to get the result:
- [tex]\[
\frac{|2r - s|}{5t + 10}
\][/tex]
Ensure the denominator \(5t + 10\) is not zero. If \(5t + 10 = 0\) (i.e., \(t = -2\)), the expression is undefined.
Thus, the solution to the expression \(\frac{|2r - s|}{5t + 10}\) involves:
1. Evaluating the absolute value of \(2r - s\).
2. Calculating \(5t + 10\).
3. Performing the division, and determining that the expression is valid only if [tex]\(5t + 10 \neq 0\)[/tex].
