Solve the Fraction Equation: 1/4x - 3 = 5 + 3/4x

To solve the equation $\frac{1}{4}x - 3 = 5 + \frac{3}{4}x$, follow these steps:

• Step 1: Eliminate $\frac{3}{4}x$ from the right side by subtracting $\frac{3}{4}x$ from both sides.

This gives:

$\frac{1}{4}x - \frac{3}{4}x - 3 = 5$

• Step 2: Combine the like terms $x$ on the left side.

This simplifies to:

$-\frac{2}{4}x - 3 = 5$

or more simply,

$-\frac{1}{2}x - 3 = 5$

• Step 3: Add 3 to both sides to move the constant term.

This results in:

$-\frac{1}{2}x = 8$

• Step 4: Solve for $x$ by multiplying both sides by $-2$ (the reciprocal of $-\frac{1}{2}$).

This yields:

$x = -16$

Therefore, the solution to the equation is $x = -16$.