Solve the following linear equations.

$$2x+5-5 = -1-5$$ $$2x = -6$$

$$\frac{2x}{2} = \frac{-6}{2}$$ $$x = -3$$

The final answer is $\boxed{-3}$.

2. $5x-4=-9$

$$5x-4+4 = -9+4$$ $$5x = -5$$

$$\frac{5x}{5} = \frac{-5}{5}$$ $$x = -1$$

The final answer is $\boxed{-1}$.

3. $\frac{2x+3}{5}=5$

$$5 \times \frac{2x+3}{5} = 5 \times 5$$ $$2x+3 = 25$$

$$2x+3-3 = 25-3$$ $$2x = 22$$

$$\frac{2x}{2} = \frac{22}{2}$$ $$x = 11$$

The final answer is $\boxed{11}$.

4. $\frac{5x-4}{2}=3$

$$2 \times \frac{5x-4}{2} = 3 \times 2$$ $$5x-4 = 6$$

$$5x-4+4 = 6+4$$ $$5x = 10$$

$$\frac{5x}{5} = \frac{10}{5}$$ $$x = 2$$

The final answer is $\boxed{2}$.

5. $\frac{x}{4}-5=x-2$

$$\frac{x}{4}-5+5 = x-2+5$$ $$\frac{x}{4} = x+3$$

$$\frac{x}{4}-x = x+3-x$$ $$\frac{x}{4}-\frac{4x}{4} = 3$$ $$-\frac{3x}{4} = 3$$

$$4 \times \left(-\frac{3x}{4}\right) = 3 \times 4$$ $$-3x = 12$$

$$\frac{-3x}{-3} = \frac{12}{-3}$$ $$x = -4$$

The final answer is $\boxed{-4}$.

6. $-\frac{4}{9}x+6=1-x$

$$-\frac{4}{9}x+6-6 = 1-x-6$$ $$-\frac{4}{9}x = -x-5$$

$$-\frac{4}{9}x+x = -x-5+x$$ $$-\frac{4}{9}x+\frac{9}{9}x = -5$$ $$\frac{5}{9}x = -5$$

$$\frac{9}{5} \times \frac{5}{9}x = -5 \times \frac{9}{5}$$ $$x = -9$$

The final answer is $\boxed{-9}$.

7. $3(x+1)=2x-4$

$$3x+3-2x = 2x-4-2x$$ $$x+3 = -4$$

$$x+3-3 = -4-3$$ $$x = -7$$

The final answer is $\boxed{-7}$.

8. $4(x-3)=2-3x$

$$4x-12+3x = 2-3x+3x$$ $$7x-12 = 2$$

$$7x-12+12 = 2+12$$ $$7x = 14$$

$$\frac{7x}{7} = \frac{14}{7}$$ $$x = 2$$

The final answer is $\boxed{2}$.