Final answer:
The equation 1/2 x 6 = 1/4 (2x - 24) simplifies to 9 = 1/2 x, which further simplifies to x = 18, giving us one unique solution.
Step-by-step explanation:
To find out how many solutions the equation 1/2 x 6 = 1/4 (2x - 24) has, we first simplify both sides and solve for x. Let's start by simplifying the equation:
First, multiply 1/2 by 6 to get 3:
3 = 1/4 (2x - 24)
Next, distribute the 1/4 across the terms in the parentheses:
3 = (1/4 × 2x) - (1/4 × 24)
3 = 1/2 x - 6
Now, add 6 to both sides of the equation to isolate the terms with x:
3 + 6 = 1/2 x
9 = 1/2 x
Finally, multiply both sides by 2 to find the value of x:
18 = x
Therefore, the equation has one unique solution, x = 18.