Solve by using number line

$$-6 > 2x \implies x < -3$$ $$2x > 2 \implies x > 1$$

We need $x < -3$ AND $x > 1$. There is no value of $x$ that satisfies both conditions simultaneously.
The solution set is empty.

$$\boxed{\text{No solution}}$$

Number line representation: Place an open circle at $-3$ and shade to the left. Place an open circle at 1 and shade to the right. There is no overlapping region.

$$\boxed{-4 < x < 2}$$

Number line representation: Place an open circle at $-4$ and an open circle at 2. Shade the region between $-4$ and 2.

$$\boxed{-3 \le x \le 5}$$

Number line representation: Place a closed circle at $-3$ and a closed circle at 5. Shade the region between $-3$ and 5.

$$\boxed{-4 < x < 8}$$

Number line representation: Place an open circle at $-4$ and an open circle at 8. Shade the region between $-4$ and 8.

$$-3 - 3 \le 3x+3 - 3 \le 9 - 3$$ $$-6 \le 3x \le 6$$

$$\boxed{-2 \le x \le 2}$$

Number line representation: Place a closed circle at $-2$ and a closed circle at 2. Shade the region between $-2$ and 2.

$$\boxed{-1 \le x \le 6}$$

Number line representation: Place a closed circle at $-1$ and a closed circle at 6. Shade the region between $-1$ and 6.

$$2y+3 - 3 < 11 - 3$$ $$2y < 8$$

$$\boxed{y < 4}$$

Number line representation: Place an open circle at 4. Shade the region to the left of 4.

$$2x-5 - 2x > 4x+7 - 2x$$ $$-5 > 2x+7$$

$$-5 - 7 > 2x+7 - 7$$ $$-12 > 2x$$

$$\boxed{-6 > x \quad \text{or} \quad x < -6}$$

Number line representation: Place an open circle at $-6$. Shade the region to the left of $-6$.