Solve the inequality and show solution sets on the real line $$-\frac{x+5}{2} \le \frac {12+3x}{4}$$
I always have issues with problems like this. I chose to ignore the negative sign at the beginning and got the answer. Is that a good method? When solving this inequality what is the best method for no mistakes?
My answer/ method: 
$$-(2)(12+3x) \le (4)(x+5)$$
$$-24-6x \le 4x+20$$
$$-24-20 \le 4x+6x$$
$$-44\le10x$$
$$-\frac{44}{10}\le x$$
$$-\frac{22}{5} \le x$$
$$\left(\infty,-\frac{22}{5}\right]$$

You have one mistake here may be typo -
$$-24+6x \le 4x+20$$
Its,  $$-24-6x \le 4x+20$$
$$-24-20 \le 4x+6x$$
$$-44 \le  10x$$
$$\frac{-22}{5} \le x$$
As the value of $x \ge \frac{-22}{5}$
$$\left[\frac{-22}{5},\infty\right)$$
