How many solutions exist for the given equation?

1/2 (x+12) = 4x-1

Distribute 1/2 throughout the set of parenthesis

1/2 · x = 1/2x

1/2 · 12 = 6

1/2x + 6 = 4x - 1

subtract 6 on both sides of the equation

1/2x = 4x - 7

subtract 1/2x by 4x

4x - 1/2x = 7/2x

7/2x = - 7

isolate x by dividing both sides by 7/2

Which is actually multiplying by the reciprocal, which is 2/7

-7 · 2/7 = - 14/2 = - 7

x = - 7

So, only one answer/solution