The inequality representing Bradley's running goal can be set up from the information provided. The total miles he needs to run is 540, and he has already run 235 miles. To express the requirement for how many additional miles (x) he needs to run, we can set up the inequality as follows:
\[ x + 235 \geq 540 \]
To isolate \(x\), we can subtract 235 from both sides of the inequality:
\[ x \geq 540 - 235 \] \[ x \geq 305 \]
Therefore, the inequality representing all possible values of \(x\) is:
\[ x \geq 305 \]
This means Bradley needs to run at least 305 more miles to reach his goal of 540 miles.