Solve the Fraction Equation: Discovering X in -1/2(x + 1/4) = 1/8

To solve the equation $-\frac{1}{2}(x+\frac{1}{4})=\frac{1}{8}$, we will first eliminate the fraction by multiplying both sides by the common denominator. The common denominator here is 8, so we proceed as follows:

• Step 1: Multiply both sides by 8 to eliminate the fractions:
  $8 \left(-\frac{1}{2}(x+\frac{1}{4})\right) = 8 \times \frac{1}{8}$
• Step 2: Simplify the left side:
  $-4(x+\frac{1}{4}) = 1$
• Step 3: Distribute $-4$ into the terms inside the parentheses:
  $-4x - 1 = 1$
• Step 4: Add 1 to both sides to isolate the term with $x$:
  $-4x = 2$
• Step 5: Divide both sides by $-4$ to solve for $x$:
  $x = \frac{2}{-4} = -\frac{1}{2}$

Therefore, the solution to the equation is $x = -\frac{1}{2}$.