f) (-7)/(8)+(2)/(3):x=(3)/(5):(12)/(-5)

To solve the equation \(\frac{-7}{8} + \frac{2}{3} : x = \frac{3}{5} : \frac{12}{-5}\), we need to follow these steps:<br /><br />1. **Simplify the right-hand side:**<br /> \[<br /> \frac{3}{5} : \frac{12}{-5} = \frac{3}{5} \times \frac{-5}{12} = \frac{3 \times -5}{5 \times 12} = \frac{-15}{60} = -\frac{1}{4}<br /> \]<br /><br />2. **Rewrite the equation with the simplified right-hand side:**<br /> \[<br /> \frac{-7}{8} + \frac{2}{3} : x = -\frac{1}{4}<br /> \]<br /><br />3. **Isolate the term involving \(x\):**<br /> \[<br /> \frac{2}{3} : x = -\frac{1}{4} - \frac{-7}{8}<br /> \]<br /> Simplify the right-hand side:<br /> \[<br /> -\frac{1}{4} + \frac{7}{8} = -\frac{2}{8} + \frac{7}{8} = \frac{5}{8}<br /> \]<br /><br />4. **Solve for \(x\):**<br /> \[<br /> \frac{2}{3} : x = \frac{5}{8}<br /> \]<br /> This means:<br /> \[<br /> \frac{2}{3} \div x = \frac{5}{8}<br /> \]<br /> So,<br /> \[<br /> x = \frac{2}{3} \div \frac{5}{8} = \frac{2}{3} \times \frac{8}{5} = \frac{2 \times 8}{3 \times 5} = \frac{16}{15}<br /> \]<br /><br />Therefore, the solution to the equation is:<br />\[<br />x = \frac{16}{15}<br />\]