Solve 2/5 (x - 1/2) = 0.25 (x + 8)

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