Solve for X: -1/4 + x = -1/2x Linear Equation Challenge

To solve the equation $-\frac{1}{4} + x = -\frac{1}{2}x$, follow these steps:

• Step 1: Begin by moving the terms involving $x$ to one side of the equation. We can do this by adding $\frac{1}{2}x$ to both sides. This gives:
  $-\frac{1}{4} + x + \frac{1}{2}x = 0$
• Step 2: Recognize that $x + \frac{1}{2}x$ can be combined into a single term:\br $-\frac{1}{4} + \frac{3}{2}x = 0$
• Step 3: Isolate $\frac{3}{2}x$ by adding $\frac{1}{4}$ to both sides, resulting in:
  $\frac{3}{2}x = \frac{1}{4}$
• Step 4: Solve for $x$ by multiplying both sides by $\frac{2}{3}$, which is the reciprocal of $\frac{3}{2}$:
  $x = \frac{1}{4} \cdot \frac{2}{3}$
• Step 5: Simplify the multiplication on the right side:
  $x = \frac{2}{12} = \frac{1}{6}$

Thus, the solution to the equation is $x = \frac{1}{6}$.