Let's analyze the given inequality step-by-step.
Given inequality:
[tex]\[
\frac{5z}{11} < 2
\][/tex]
We need to isolate [tex]\( z \)[/tex]. To do this, we will eliminate the fraction by multiplying both sides of the inequality by 11, the denominator of the fraction on the left side. This gives us:
[tex]\[
5z < 2 \cdot 11
\][/tex]
Simplifying the right-hand side, we get:
[tex]\[
5z < 22
\][/tex]
Next, we need to solve for [tex]\( z \)[/tex] by isolating it. We do this by dividing both sides of the inequality by 5:
[tex]\[
z < \frac{22}{5}
\][/tex]
Calculating the numerical value of [tex]\( \frac{22}{5} \)[/tex]:
[tex]\[
\frac{22}{5} = 4.4
\][/tex]
Therefore, the solution set for the given inequality is:
[tex]\[
\{ z \mid z < \frac{22}{5} \}
\][/tex]
or equivalently,
[tex]\[
\{ z \mid z < 4.4 \}
\][/tex]
Among the given options, the correct solution set is:
\[
\{ x \mid x < \frac{22}{5} \}
