Solve for X: Finding the Value in (1/3)x - (1/2)x = 3

To solve this problem, we'll follow these steps:

• Step 1: Find a common denominator for the fractions involved.
• Step 2: Simplify the left-hand side of the equation.
• Step 3: Solve the resulting equation for $x$.

Now, let's work through each step:

Step 1: The given equation is $\frac{1}{3}x - \frac{1}{2}x = 3$. The fractions $\frac{1}{3}$ and $\frac{1}{2}$ need a common denominator. The least common denominator for 3 and 2 is 6.

Step 2: Convert each fraction: $\frac{1}{3} = \frac{2}{6} \quad \text{and} \quad \frac{1}{2} = \frac{3}{6}$ Thus, the equation $\frac{1}{3}x - \frac{1}{2}x = 3$ becomes $\frac{2}{6}x - \frac{3}{6}x = 3$ Combine the terms: $\left(\frac{2}{6} - \frac{3}{6}\right)x = -\frac{1}{6}x$ So the equation is: $-\frac{1}{6}x = 3$

Step 3: Solve for $x$: To isolate $x$, multiply both sides of the equation by $-6$ (the reciprocal of $-\frac{1}{6}$): $x = 3 \times (-6)$ $x = -18$

Therefore, the solution to the problem is $x = -18$.