Final answer:
To solve the equation 1/2x + 6 = 1/4 (2x - 24), distribute the 1/4 to both terms inside the parentheses, simplify the equation, and subtract 1/2x from both sides. The resulting equation, 6 = -6, is not true, indicating that there are no solutions.
Step-by-step explanation:
To solve the equation 1/2x + 6 = 1/4 (2x - 24), you can start by distributing the 1/4 to both terms inside the parentheses:
1/2x + 6 = 1/4 * 2x - 1/4 * 24
Simplifying further:
1/2x + 6 = 1/2x - 6
Next, subtract 1/2x from both sides of the equation:
6 = - 6
Since the equation 6 = - 6 is not true, there are no solutions to this equation.