Solve for X: Finding the Value in (1/4)x - (2/3)x + (1/8)x = 5

Solve the equation by following these steps:

• Step 1: Find the least common multiple (LCM) of the denominators $4$, $3$, and $8$. The LCM is $24$.
• Step 2: Rewrite each term so that the denominator is $24$.
  $\frac{1}{4}x = \frac{6}{24}x$
  $-\frac{2}{3}x = -\frac{16}{24}x$
  $\frac{1}{8}x = \frac{3}{24}x$
• Step 3: Combine the terms over the common denominator:
  $\left(\frac{6}{24} - \frac{16}{24} + \frac{3}{24}\right)x = 5$
• Step 4: Simplify the left side:
  $\frac{6 - 16 + 3}{24}x = 5$
  $\frac{-7}{24}x = 5$
• Step 5: Solve for $x$ by isolating it:
  Multiply both sides by $-24/7$:
  $x = 5 \times \left(-\frac{24}{7}\right)$
• Step 6: Perform the multiplication:
  $x = -\frac{120}{7}$
• Step 7: Convert the improper fraction to a mixed number:
  The mixed number is $-17\frac{1}{7}$.

The solution to the equation is $x = -17\frac{1}{7}$.