Answer:
z = 14
Explanation:
Solve for z:
(4 z)/7 - 15 = -7
Put each term in (4 z)/7 - 15 over the common denominator 7: (4 z)/7 - 15 = (4 z)/7 - 105/7:
(4 z)/7 - 105/7 = -7
(4 z)/7 - 105/7 = (4 z - 105)/7:
1/7 (4 z - 105) = -7
Multiply both sides of (4 z - 105)/7 = -7 by 7:
(7 (4 z - 105))/7 = -7×7
(7 (4 z - 105))/7 = 7/7×(4 z - 105) = 4 z - 105:
4 z - 105 = -7×7
7 (-7) = -49:
4 z - 105 = -49
Add 105 to both sides:
4 z + (105 - 105) = 105 - 49
105 - 105 = 0:
4 z = 105 - 49
105 - 49 = 56:
4 z = 56
Divide both sides of 4 z = 56 by 4:
(4 z)/4 = 56/4
4/4 = 1:
z = 56/4
The gcd of 56 and 4 is 4, so 56/4 = (4×14)/(4×1) = 4/4×14 = 14:
Answer: z = 14