Solve for X: Finding the Value in (1/8)x + (2/3)x = 3

To solve the equation $\frac{1}{8}x + \frac{2}{3}x = 3$, we need to clear the fractions by finding the least common denominator.

Step 1: Identify the least common denominator of the fractions.
The denominators are 8 and 3. The least common denominator (LCD) is 24.

Step 2: Rewrite the equation with the LCD to get rid of the fractions:
Multiply each term by 24:
$24 \times \frac{1}{8} x + 24 \times \frac{2}{3} x = 24 \times 3$.

Step 3: Simplify each term:
$\frac{24}{8}x = 3x$,
$\frac{24}{3}x = 16x$,
Thus, the equation becomes $3x + 16x = 72$.

Step 4: Combine like terms:
$19x = 72$.

Step 5: Solve for $x$ by dividing both sides by 19:
$x = \frac{72}{19}$.

Convert the improper fraction to a mixed number:
Divide 72 by 19, which gives 3 with a remainder of 15. Thus, $x = 3\frac{15}{19}$.

Therefore, the solution to the problem is $x = 3\frac{15}{19}$.