Answer:
x = 7
Explanation:
Solve for x:
8 (x - 3) - 3 (x - 1) = 6 x - 5 x + 7
-3 (x - 1) = 3 - 3 x:
3 - 3 x + 8 (x - 3) = 6 x - 5 x + 7
8 (x - 3) = 8 x - 24:
8 x - 24 - 3 x + 3 = 6 x - 5 x + 7
Grouping like terms, 8 x - 3 x - 24 + 3 = (8 x - 3 x) + (3 - 24):
(8 x - 3 x) + (3 - 24) = 6 x - 5 x + 7
8 x - 3 x = 5 x:
5 x + (3 - 24) = 6 x - 5 x + 7
3 - 24 = -21:
5 x + -21 = 6 x - 5 x + 7
Grouping like terms, 6 x - 5 x + 7 = (6 x - 5 x) + 7:
5 x - 21 = (6 x - 5 x) + 7
6 x - 5 x = x:
5 x - 21 = x + 7
Subtract x from both sides:
(5 x - x) - 21 = (x - x) + 7
5 x - x = 4 x:
4 x - 21 = (x - x) + 7
x - x = 0:
4 x - 21 = 7
Add 21 to both sides:
4 x + (21 - 21) = 21 + 7
21 - 21 = 0:
4 x = 7 + 21
7 + 21 = 28:
4 x = 28
Divide both sides of 4 x = 28 by 4:
(4 x)/4 = 28/4
4/4 = 1:
x = 28/4
The gcd of 28 and 4 is 4, so 28/4 = (4×7)/(4×1) = 4/4×7 = 7:
Answer: x = 7