Solve for x

2 (3x-4) = 4 (1/2x-8)

x = - 6

Step-by-step explanation:

Solve for x:

2 (3 x - 4) = 4 (x/2 - 8)

Put each term in x/2 - 8 over the common denominator 2: x/2 - 8 = x/2 - 16/2:

2 (3 x - 4) = 4 x/2 - 16/2

x/2 - 16/2 = (x - 16) / 2:

2 (3 x - 4) = 4 (x - 16) / 2

4/2 = (2*2) / 2 = 2:

2 (3 x - 4) = 2 (x - 16)

Divide both sides by 2:

3 x - 4 = x - 16

Subtract x from both sides:

(3 x - x) - 4 = (x - x) - 16

3 x - x = 2 x:

2 x - 4 = (x - x) - 16

x - x = 0:

2 x - 4 = - 16

Add 4 to both sides:

2 x + (4 - 4) = 4 - 16

4 - 4 = 0:

2 x = 4 - 16

4 - 16 = - 12:

2 x = - 12

Divide both sides of 2 x = - 12 by 2:

(2 x) / 2 = (-12) / 2

2/2 = 1:

x = (-12) / 2

The gcd of - 12 and 2 is 2, so (-12) / 2 = (2 (-6)) / (2*1) = 2/2*-6 = - 6:

Answer: x = - 6