Algebra 3 Test \( \frac{1}{4 x}-\frac{3}{4}=\frac{7}{x} \)

To solve the equation \( \frac{1}{4 x}-\frac{3}{4}=\frac{7}{x} \), we first eliminate the fractions by multiplying through by \( 4x \) (the least common multiple of the denominators). This results in \( 1 - 3x = 28 \). Rearranging gives us \( -3x = 27 \), leading to \( x = -9 \). Now, let’s double-check our solution: substituting \( x = -9 \) back into the original equation should hold true! To avoid common mistakes when solving similar equations, always ensure you correctly multiply through by the appropriate least common denominator. A small slip in arithmetic or sign can lead to very different results, so keep a keen eye on your calculations!