1. **Stating the problem:** We are given five equations and asked to find which one is the odd one out. 2. **Analyzing each equation:** - Equation 1: $3(x+1)^2 = 10$ - Equation 2: $3x = \frac{7}{x+2}$ - Equation 3: $x = \sqrt{\frac{7 - 6x}{3}}$ - Equation 4: $x = \frac{7 + 6x}{3x}$ - Equation 5: $x = \frac{7 - 3x^2}{6}$ 3. **Observing the structure:** - Equations 1, 2, 3, and 5 can be rearranged or simplified into polynomial or radical forms involving $x$. - Equation 4 has $x$ on both numerator and denominator on the right side, making it a rational expression with $x$ in the denominator. 4. **Checking for domain restrictions:** - Equation 4 has a denominator $3x$, so $x \neq 0$. - Other equations do not have $x$ in the denominator. 5. **Checking the type of equations:** - Equations 1, 3, and 5 are polynomial or radical equations. - Equation 2 is a rational equation but with $x+2$ in the denominator. - Equation 4 is a rational equation with $x$ in the denominator, which is different from others. 6. **Conclusion:** Equation 4 is the odd one out because it has $x$ in the denominator on the right side, which imposes a domain restriction and a different structure compared to the others. **Final answer:** Equation 4 is the odd one out.