Solve for z:
42 = -7 (z - 3)
42 = -7 (z - 3) is equivalent to -7 (z - 3) = 42:
-7 (z - 3) = 42
Divide both sides of -7 (z - 3) = 42 by -7:
(-7 (z - 3))/(-7) = 42/(-7)
(-7)/(-7) = 1:
z - 3 = 42/(-7)
The gcd of 42 and -7 is 7, so 42/(-7) = (7×6)/(7 (-1)) = 7/7×6/(-1) = 6/(-1):
z - 3 = 6/(-1)
Multiply numerator and denominator of 6/(-1) by -1:
z - 3 = -6
Add 3 to both sides:
z + (3 - 3) = 3 - 6
3 - 3 = 0:
z = 3 - 6
3 - 6 = -3:
Answer: z = -3
