Question

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

Answer 1

Answer:

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