Solve for X: Combining -1/4x + 2/3x - 1/6x = 2

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

• Step 1: Identify the common denominator.
• Step 2: Rewrite the equation with the common denominator.
• Step 3: Combine like terms.
• Step 4: Solve the simplified equation for $x$.

Now, let's work through each step:

Step 1: The denominators of the fractions are 4, 3, and 6. The least common denominator is 12.

Step 2: Rewrite each term with the common denominator:

• $-\frac{1}{4}x = -\frac{3}{12}x$
• $\frac{2}{3}x = \frac{8}{12}x$
• $-\frac{1}{6}x = -\frac{2}{12}x$

Step 3: Combine the fractions:

$-\frac{3}{12}x + \frac{8}{12}x - \frac{2}{12}x = 2$

This simplifies to $\frac{3}{12}x = 2$.

Step 4: Simplify and solve for $x$:

Multiply both sides by 12 to clear the denominator:

$3x = 24$

Divide both sides by 3:

$x = 8$

Therefore, the solution to the problem is $x = 8$.