How do you solve x/2+1=1/4x-6?

To solve the equation x/2 + 1 = 1/4x - 6, we need to isolate the variable x on one side of the equation. Here's the step-by-step solution:

Step 1: Clear the fractions
To eliminate the fractions, we can multiply every term by the least common denominator (LCD), which is 4. Multiplying each term by 4, the equation becomes:
4 * (x/2) + 4 * 1 = 4 * (1/4x) - 4 * 6
2x + 4 = x - 24

Step 2: Combine like terms
Next, we combine like terms on both sides of the equation:
2x - x = -24 - 4
x = -28

Step 3: Check the solution
To confirm the solution, substitute the value of x back into the original equation:
(-28)/2 + 1 = (1/4 * -28) - 6
-14 + 1 = -7 - 6
-13 = -13

Since the equation is true when x = -28, the solution is verified.

Therefore, the solution to the equation x/2 + 1 = 1/4x - 6 is x = -28.