Our inequality is [tex] \frac{1}{2} x -2 > 0 [/tex]. We first clear fractions - because nobody likes fractions - and multiply the whole inequality by 2. 2 is chosen because it's the least common denominator of (from right to left) 1, 1, and 2.
[tex] \frac{1}{2} x -2 > 0 [/tex].
x - 4 > 0 after multiplying through by 2
x > 4
On the number line we want all things more than 4. We want an open (or unfilled circle) too - that's because 4 is not included in the answer.
The third choice shows a red line over things to the right of 4 - - or more than 4. It has an open circle. That's our solution set.
Thus, the third choice is the best answer.
