This is an inequality problem. The way to solve this is to treat the inequality sign (<, >, etc) like an equal sign (=).
-7z - 7 = -5z + 5
first, you get rid of the constants (the numbers that don't have variables with them)
the way to do that is to perform reverse operations (when there is a negative, add. when positive, subtract. same for multiplying and dividing)
-7z - 7 = -5z + 5
+ 7 + 7
------------------------
-7z = -5z + 12
the sevens are cancelled out because of the + and the - on both of them, and 5+7 is 12.
now, for the coefficients. you do the same process.
-7z - 7 = -5z + 5
+ 7 + 7
------------------------
-7z = -5z + 12
+5z +5z
-------------------------
-2z = 12
now that you have combined all the alike terms, you divide until the variable is by itself. (/ is divide)
-7z - 7 = -5z + 5
+ 7 + 7
------------------------
-7z = -5z + 12
+5z +5z
-------------------------
-2z = 12
/-2 /-2
-----------------------
z = -6
twelve divided by -2 is -6. so, z = -6.
now all you have to do is switch out the inequality sign: z < -6