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

Subtracting $\frac{3}{4}x$ from both sides keeps the equation balanced while collecting all x-terms on one side. This is the key to isolating the variable!

When fractions have the same denominator, just subtract the numerators: $\frac{1}{4} - \frac{3}{4} = \frac{1-3}{4} = \frac{-2}{4} = -\frac{1}{2}$. Keep the denominator the same!

To solve $-\frac{1}{2}x = 8$, multiply both sides by -2: $x = 8 \times (-2) = -16$. Remember that multiplying by -2 flips the sign!

Yes! You could add 3 to both sides first, then subtract the variable terms. Either order works - just be consistent and keep the equation balanced at each step.

Negative answers are completely normal! In this problem, the coefficient of x becomes negative ($-\frac{1}{2}$), and we're solving $-\frac{1}{2}x = 8$, so x must be negative to make this true.