To solve the problem of finding the value of [tex]\( x \)[/tex] for which the class mark of the class interval [tex]\( 30 - x \)[/tex] is 36, we need to understand what a class mark is. The class mark (or midpoint) of a class interval is calculated as the average of the lower and the upper class limits.
For the class interval [tex]\( 30 - x \)[/tex], the formula for the class mark is:
[tex]\[
\text{Class Mark} = \frac{\text{Lower Limit} + \text{Upper Limit}}{2}
\][/tex]
Given that the class mark is 36, let’s set up the equation:
[tex]\[
\frac{30 + x}{2} = 36
\][/tex]
To solve for [tex]\( x \)[/tex], follow these steps:
1. Multiply both sides of the equation by 2 to eliminate the fraction:
[tex]\[
30 + x = 72
\][/tex]
2. Subtract 30 from both sides to isolate [tex]\( x \)[/tex]:
[tex]\[
x = 72 - 30
\][/tex]
3. Simplify the right-hand side:
[tex]\[
x = 42
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] for which the class mark of the class interval [tex]\( 30 - x \)[/tex] is 36 is:
\[
\boxed{42}
