To solve the inequality [tex]\(\frac{7x}{2} < 5\)[/tex], let's go through the steps one by one:
1. Remove the fraction by eliminating the denominator:
To eliminate the denominator 2, we multiply both sides of the inequality by 2.
[tex]\[
2 \cdot \frac{7x}{2} < 2 \cdot 5
\][/tex]
Simplifying, we get:
[tex]\[
7x < 10
\][/tex]
2. Isolate [tex]\( x \)[/tex] on one side:
To isolate [tex]\( x \)[/tex], we divide both sides of the inequality by 7.
[tex]\[
\frac{7x}{7} < \frac{10}{7}
\][/tex]
Simplifying, we get:
[tex]\[
x < \frac{10}{7}
\][/tex]
3. Solution set:
The solution to the inequality [tex]\( x < \frac{10}{7} \)[/tex] can be written in set notation as:
[tex]\[
\{x \mid x < \frac{10}{7}\}
\][/tex]
Given the options, the correct solution set is:
[tex]\[
\{x \mid x < \frac{10}{7}\}
\][/tex]
So, the correct choice is [tex]\(\{x \mid x < \frac{10}{7}\}\)[/tex].
