2(x - 1) – 7x = 18 – 5(x + 4

$$\begin{array}{rll}
2(x - 1)-7x&=&18-5(x + 4)\\\\
2x-2-7x&=&18+[-5(x + 4)]\\\\
-2-5x&=&18+[-5x+-20]\\\\
-2-5x&=&18+[-5x-20]\\\\
-2-5x&=&18-5x-20\\\\
-2-5x&=&-2-5x\\\\
\end{array}$$

Here I can see that both sides are identical.  This means that this will be true for EVERY value of x.

 2(x - 1) – 7x = 18 – 5(x + 4)

2x - 2 - 7x = 18 - 5x - 20

-5x - 2  =  -2 - 5x      add 5x to both sides

-2  = -2

This is an identity.....and as Melody has said, is true for all real x