#-27x - 67 = 122 - 24x#

First, you want to remove the variable of the lowest value so that way you can solve this as a two-step equation. In this case, the variable with the lowest value is #-27x#. In order to get rid of it, we'll add #27x# to cancel out the #-27#. Because you add to one side, you must add to the other side to become equal. So, #27x - 24x = 3x# on the right side. Your equation should now look like this:

#-67 = 122 + 3x#

Now, subtract #122# from both sides to cancel out #122# in order to isolate for #x#. #-67 - 122 = -189#. Recall that two numbers of the same sign technically add up. Your equation should now look like this:

#-189 = 3x#

Now, divide by #3# in order to isolate for #x#. #3/3# = #1#, and #-189/3# = #-63#, so this will be the value of your variable.

#x = -63#

To verify that #x# *really is* #-63#, we'll plug it back into the equation. Replace #x# with the value #-63#.

#-27x - 67 = 122 - 24x#

#-27(-63) - 67 = 122 -24(-63)#

#1701 - 67 = 122 + 1512#

#1634 = 1634#

#x = -63#