Questions: Decide whether the given number is a solution of the equation. Is 1/3 a solution of (x+10)/(9-x)=31/26 ? Choose the correct answer below. Yes No

Solution Steps

To determine if \(\frac{1}{3}\) is a solution to the equation \(\frac{x+10}{9-x}=\frac{31}{26}\), we substitute \(x = \frac{1}{3}\) into the equation and check if both sides are equal. If they are equal, then \(\frac{1}{3}\) is a solution; otherwise, it is not.

We substitute \( x = \frac{1}{3} \) into the equation \( \frac{x+10}{9-x} = \frac{31}{26} \).

Calculating the left side: \[ \text{Left Side} = \frac{\frac{1}{3} + 10}{9 - \frac{1}{3}} = \frac{\frac{1}{3} + \frac{30}{3}}{\frac{27}{3} - \frac{1}{3}} = \frac{\frac{31}{3}}{\frac{26}{3}} = \frac{31}{26} \]

Now we compare the left side with the right side: \[ \text{Left Side} = \frac{31}{26}, \quad \text{Right Side} = \frac{31}{26} \] Since both sides are equal, we conclude that \( \frac{1}{3} \) is indeed a solution to the equation.

Final Answer