Answer:
x = 2
Explanation:
Solve for x:
5 (3 - x) - 2 (4 - 3 x) = 11 - 2 (x - 1)
5 (3 - x) = 15 - 5 x:
15 - 5 x - 2 (4 - 3 x) = 11 - 2 (x - 1)
-2 (4 - 3 x) = 6 x - 8:
6 x - 8 - 5 x + 15 = 11 - 2 (x - 1)
Grouping like terms, 6 x - 5 x - 8 + 15 = (-5 x + 6 x) + (15 - 8):
(-5 x + 6 x) + (15 - 8) = 11 - 2 (x - 1)
6 x - 5 x = x:
x + (15 - 8) = 11 - 2 (x - 1)
15 - 8 = 7:
x + 7 = 11 - 2 (x - 1)
-2 (x - 1) = 2 - 2 x:
x + 7 = 2 - 2 x + 11
Grouping like terms, -2 x + 2 + 11 = (11 + 2) - 2 x:
x + 7 = (11 + 2) - 2 x
11 + 2 = 13:
x + 7 = 13 - 2 x
Add 2 x to both sides:
2 x + x + 7 = (2 x - 2 x) + 13
2 x - 2 x = 0:
2 x + x + 7 = 13
Grouping like terms, 2 x + x + 7 = (x + 2 x) + 7:
(x + 2 x) + 7 = 13
x + 2 x = 3 x:
3 x + 7 = 13
Subtract 7 from both sides:
3 x + (7 - 7) = 13 - 7
7 - 7 = 0:
3 x = 13 - 7
13 - 7 = 6:
3 x = 6
Divide both sides of 3 x = 6 by 3:
(3 x)/3 = 6/3
3/3 = 1:
x = 6/3
The gcd of 6 and 3 is 3, so 6/3 = (3×2)/(3×1) = 3/3×2 = 2:
Answer: x = 2