Answer:
The solution to the equation (1/6)x - 3 = (1/2)(x + 18) is x = -36.
Explanation:
To solve the equation (1/6)x - 3 = (1/2)(x + 18), we will follow these steps:
Distribute the 1/2 to both terms inside the parentheses on the right side of the equation:
(1/6)x - 3 = (1/2)x + 9.
Let's simplify the equation by multiplying every term by the least common denominator (LCD) of 6 to eliminate the fractions:
6 * ((1/6)x) - 6 * 3 = 6 * ((1/2)x) + 6 * 9.
This simplifies to:
x - 18 = 3x + 54.
Now, we will gather the x terms on one side of the equation and the constant terms on the other side. Subtract 3x from both sides and add 18 to both sides:
x - 3x = 54 + 18.
Simplifying further, we get:
-2x = 72.
Divide both sides of the equation by -2 to isolate x:
(-2x) / -2 = 72 / -2.
This simplifies to:
x = -36.
Therefore, the solution to the equation (1/6)x - 3 = (1/2)(x + 18) is x = -36.