Get the variable you want solved for isolated on one side of the equation (this is typically done on the left-hand side) and the value of the variable will be on the opposite side (usually the right-hand side).
We want x solved for.
-3 + 4x = -5 - 6x
You can tackle this problem from different ways, but the best way to do this is to find the shortest route to the answer. We can either take the 4x on the left-hand side, subtract from both sides and the 4x on the left-hand side will vanish. Another way to do it is to look at the -5 on the right-hand side and say, "What will I have to add to -5 to make it disappear?" This number is called the Additive Inverse and is the opposite of an integer. The sum of an integer and its Additive Inverse is 0. The opposite of -5 is -(-5) or simply 5. We can add that to both sides of the equation to have -5 on the right-hand side to disappear.
We can actually do one of these options and then do the other.
-3 + 4x = -5 - 6x
First, subtract 4x from each side.
(-3 + 4x) - 4x = (-5 - 6x) - 4x
-3 = -5 - 10x
Now add 5 to each side.
-3 + 5 = (-5 - 10x) + 5
2 = -10x
Finally, divide both sides by -10.
2 / -10 = -10x / -10
-(1/5) = x
If you want this to look more like the traditional variable on the left and value of the right, we can apply the symmetric law of equality.
x = -(1/5)