\( \frac { 3 ) } { 3 x + 4 } = \frac { 2 x - 8 } { 3 } \)

To solve the equation \( \frac{3}{3x + 4} = \frac{2x - 8}{3} \), you can start by cross-multiplying to eliminate the fractions. This leads to the equation \( 3 \times (2x - 8) = (3x + 4) \times 3 \). Simplifying both sides, you get \( 6x - 24 = 9x + 12 \). Rearranging gives \( 6x - 9x = 12 + 24 \), resulting in \( -3x = 36 \), thus \( x = -12 \). To check your solution, you can substitute \( x = -12 \) back into the original equation. For the left-hand side, you’ll get \( \frac{3}{3(-12) + 4} = \frac{3}{-36 + 4} = \frac{3}{-32} \). For the right-hand side, \( \frac{2(-12) - 8}{3} = \frac{-24 - 8}{3} = \frac{-32}{3} \). If these simplified versions equal each other, your solution is correct!