1/4x + x = - 3 + 1/2x, what is x?

x = - 4

Step-by-step explanation:

Solve for x:

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

Put each term in x/2 - 3 over the common denominator 2: x/2 - 3 = x/2 - 6/2:

(5 x) / 4 = x/2 - 6/2

x/2 - 6/2 = (x - 6) / 2:

(5 x) / 4 = (x - 6) / 2

Multiply both sides by 4:

(4*5 x) / 4 = (4 (x - 6)) / 2

(4*5 x) / 4 = 4/4*5 x = 5 x:

5 x = (4 (x - 6)) / 2

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

5 x = 2 (x - 6)

Expand out terms of the right hand side:

5 x = 2 x - 12

Subtract 2 x from both sides:

5 x - 2 x = (2 x - 2 x) - 12

5 x - 2 x = 3 x:

3 x = (2 x - 2 x) - 12

2 x - 2 x = 0:

3 x = - 12

Divide both sides of 3 x = - 12 by 3:

(3 x) / 3 = (-12) / 3

3/3 = 1:

x = (-12) / 3

The gcd of - 12 and 3 is 3, so (-12) / 3 = (3 (-4)) / (3*1) = 3/3*-4 = - 4:

Answer: x = - 4