Answer :

GinnyAnswer
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].

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