The image you uploaded contains a problem involving solving an equation and verifying whether a student's steps are correct. Let's analyze the equation and the steps described in the image.

Given Equation:

$\frac{x}{4} + \frac{7}{3} = x$

Steps Described:

1. Subtract $\frac{x}{4}$ from both sides: $\frac{7}{3} = x - \frac{x}{4}$

2. Multiply by 4: $\frac{28}{3} = 4x - x$

3. Conclusion: $\frac{28}{3} = 3x$

The student wants to determine whether this final equation is correct and whether their steps are valid.

Solution Verification:

1. Step 1: Subtracting $\frac{x}{4}$ from both sides is correct. The new equation: $\frac{7}{3} = x - \frac{x}{4}$

2. Step 2: The student needs to combine the terms on the right-hand side. Notice that: $x - \frac{x}{4} = \frac{4x - x}{4} = \frac{3x}{4}$ So the equation becomes: $\frac{7}{3} = \frac{3x}{4}$

3. Step 3: Multiply both sides by 4 to eliminate the denominator on the right-hand side: $\frac{28}{3} = 3x$

This matches the student's conclusion. Therefore, the student's solution is correct.

How Can Delta Determine if the Solution is Correct?

Delta can determine if the solution is correct by checking if the operations applied in each step are algebraically sound and lead to a logically equivalent expression. In this case, the operations were correct, leading to the correct conclusion.

Do you want more details or have any questions?

Here are 5 related questions:

1. How would you solve the equation if the fractions were more complex?
2. What is the importance of keeping track of signs when solving equations?
3. How can you verify your solution after solving an equation?
4. How would the solution change if the equation included a constant on both sides?
5. What are common mistakes to avoid when solving algebraic equations?

Tip: Always double-check your work by substituting your solution back into the original equation to ensure it holds true.