With a Fraction

To solve $\frac{x}{2}-1 > 3$, add 1 to both sides, then multiply both sides by 2. Neither step changes the sign, because 2 is positive:

$$\frac{x}{2} > 4$$

$$x > 8$$

You can also clear the fraction first. Multiply every term by 2 to get $x-2 > 6$, then add 2 to both sides. This gives the same answer in the same number of steps.

When a whole side is one fraction, clearing the denominator is a good first step. For $\frac{x+1}{3} \le 2$, multiply both sides by 3 to get $x+1 \le 6$. Then subtract 1 from both sides to get $x \le 5$.