Solve for x:
(2 (x - 1/2))/5 = 0.25 (x + 8)
Put each term in x - 1/2 over the common denominator 2: x - 1/2 = (2 x)/2 - 1/2:
2/5 (2 x)/2 - 1/2 = 0.25 (x + 8)
(2 x)/2 - 1/2 = (2 x - 1)/2:
2/5 (2 x - 1)/2 = 0.25 (x + 8)
(2 (2 x - 1))/(2×5) = 2/2×(2 x - 1)/5 = (2 x - 1)/5:
(2 x - 1)/5 = 0.25 (x + 8)
Multiply both sides by 5:
(5 (2 x - 1))/5 = 5×0.25 (x + 8)
(5 (2 x - 1))/5 = 5/5×(2 x - 1) = 2 x - 1:
2 x - 1 = 5×0.25 (x + 8)
5×0.25 = 1.25:
2 x - 1 = 1.25 (x + 8)
Expand out terms of the right hand side:
2 x - 1 = 1.25 x + 10.
Subtract 1.25 x from both sides:
(2 x - 1.25 x) - 1 = (1.25 x - 1.25 x) + 10.
2 x - 1.25 x = 0.75 x:
0.75 x - 1 = (1.25 x - 1.25 x) + 10.
1.25 x - 1.25 x = 0:
0.75 x - 1 = 10.
Add 1 to both sides:
0.75 x + (1 - 1) = 1 + 10.
1 - 1 = 0:
0.75 x = 10. + 1
10. + 1 = 11.:
0.75 x = 11.
Divide both sides of 0.75 x = 11. by 0.75:
(0.75 x)/0.75 = 11./0.75
0.75/0.75 = 1:
x = 11./0.75
11./0.75 = 14.6667:
Answer: x = 14.6667
