We are trying to solve for x which is an unknown variable. If you plug x (after you solve it) back into the equation then one side of the equation should equal the other side. (9 = 9)
In algebra we go by the PEMDAS rule. Parenthesis first. You can do this by using the distributive property.
4(x +1) - 5x - 4 = 9
Remember distributive property is multiplying what is outside the parenthesis by what is inside. So 4 times x is 4x and 4 times 1 is 4. You write this out and what is left over that you haven't solved yet.
4x + 4 - 5x - 4 = 9
This is what we have so far. Now we can either add up like terms (every number with an x attached to it), or add constants (regular plain numbers without x attached to it) or if you're really pro you can do both at the same time.
So like terms first:
4x - 5x is the same thing as 4 - 5 which is -1, so you get
-1x + 4 - 4 = 9
Now constants: 4 -4 = 0 so you don't have to write anything it just disappears, it's zero!
Now what we have so far is
-1x = 9
And what we do next is divide -1x by -1 and then divide the number on the other side (in this case 9) also by -1. Therefore
(cancel(-1)x)/cancel(-1) = 9/(-1)
When we solve this (9 / (-1)) we get -9, so -9 is the answer.
x = -9
Like I said at the beginning, if you plug -9 back into the equation, if your problem solving was right, then one side should equal the other one. And when we plug -9 into the parenthesis and solve the left side of the equation, 9 = 9, so we know for sure our answer is right.
Happy hunting!
