1. **State the problem:** We are given the expression $-5 + \frac{7x}{4}$ and a table of values for $x$ and the expression's value. We need to identify which algebraic expression from the options A to F matches the given expression and table. 2. **Analyze the given expression:** The expression is $-5 + \frac{7x}{4}$. 3. **Check the options:** - A: $\frac{7}{4}x - 5$ is equivalent to $-5 + \frac{7x}{4}$ (just reordered). - B: $(-5 + 7) + \frac{x}{4} = 2 + \frac{x}{4}$, which does not match. - C: $\frac{7x - 5}{4}$ is different because the $-5$ is divided by 4. - D: $5 + \left(-\frac{7x}{4}\right) = 5 - \frac{7x}{4}$, which is different. - E: $\frac{4}{-5} + 7x = -\frac{4}{5} + 7x$, different. - F: $\frac{7x}{4} + (-5) = -5 + \frac{7x}{4}$, same as original. 4. **Verify with table values:** - For $x=0$, expression $= -5 + \frac{7\times0}{4} = -5$ matches table. - For $x=8$, expression $= -5 + \frac{7\times8}{4} = -5 + 14 = 9$ matches table. - For $x=16$, expression $= -5 + \frac{7\times16}{4} = -5 + 28 = 23$ matches table. 5. **Conclusion:** Options A and F represent the expression correctly. **Final answer:** The expression is $-5 + \frac{7x}{4}$, which matches options A and F. $$\boxed{-5 + \frac{7x}{4}}$$