This is just solving an equation. The first thing you want to do is get x all by itself on one side. To do this, we would subtract x from both sides.
$$-6x-x=x+4-x$$
On the left, -6x-x would simplify to -7x. On the right, the two x's (note that they are opposite signs: one positive and one negative!) would cancel out, leaving no x's on that side. Now, we have the equation:$$-7x=4$$
Now, we want x to be all by itself, without that -7 right next to it. Well, what's the opposite of multiplication? Division! So, let's divide both sides by -7 and see what happens.$$\frac{-7x}{-7}=\frac{4}{-7}\Rightarrow x=\frac{-4}{7}\approx -0.571$$
And there we go! That's what x needs to equal for this equation to be true!