Master the Equation: Solve 1/8X + 3 = -1/5 + 5/16X

To solve the equation $\frac{1}{8}x + 3 = -\frac{1}{5} + \frac{5}{16}x$, we will perform the following steps:

• Step 1: Clear the fractions
  First, find the least common multiple (LCM) of the denominators 8, 5, and 16. The LCM is 80.
• Step 2: Eliminate the fractions
  Multiply every term in the equation by 80:
$80 \times \frac{1}{8}x + 80 \times 3 = 80 \times \left(-\frac{1}{5}\right) + 80 \times \frac{5}{16}x$
• Simplifying, we get:
$10x + 240 = -16 + 25x$
• Step 3: Rearrange and combine like terms
  Subtract $10x$ from both sides to get the $x$ terms on one side:
$240 = -16 + 25x - 10x$
• Further simplifying, we have:
$240 = -16 + 15x$
• Add 16 to both sides to isolate terms with $x$:
$240 + 16 = 15x$ $256 = 15x$
• Step 4: Solve for $x$
  Divide both sides by 15:
$x = \frac{256}{15}$

Therefore, the solution to the equation is $x = \frac{256}{15}$. The correct choice corresponding to this answer is choice 2.