The equation displayed in the image is:

$\left( -3 \frac{1}{2} \right) - \left( -4 \frac{1}{4} \right) = \frac{7}{2} - \left( -\frac{17}{4} \right)$

Let's solve it step by step.

Step 1: Convert mixed fractions to improper fractions

• $-3 \frac{1}{2} = -\frac{7}{2}$
• $-4 \frac{1}{4} = -\frac{17}{4}$

Thus, the equation becomes:

$\left( -\frac{7}{2} \right) - \left( -\frac{17}{4} \right) = \frac{7}{2} - \left( -\frac{17}{4} \right)$

Step 2: Simplify both sides

• On the left-hand side: $-\frac{7}{2} - (-\frac{17}{4}) = -\frac{7}{2} + \frac{17}{4}$

  To add these fractions, get a common denominator. The least common denominator between 2 and 4 is 4:

  $-\frac{7}{2} = -\frac{14}{4}$

  So now the expression becomes: $-\frac{14}{4} + \frac{17}{4} = \frac{3}{4}$

• On the right-hand side: $\frac{7}{2} - (-\frac{17}{4}) = \frac{7}{2} + \frac{17}{4}$

  Again, get a common denominator: $\frac{7}{2} = \frac{14}{4}$

  So the expression becomes: $\frac{14}{4} + \frac{17}{4} = \frac{31}{4}$

Final result:

The equation simplifies to:

$\frac{3}{4} = \frac{31}{4}$

This equation is false, as $\frac{3}{4} \neq \frac{31}{4}$. Therefore, the original equation does not hold.

Would you like more details on any specific part of the solution?

Here are 5 related questions to expand on this:

1. How do you add or subtract fractions with different denominators?
2. What is the process for converting mixed numbers to improper fractions?
3. How do you solve equations involving fractions on both sides?
4. Can you solve more complex equations with fractions and variables?
5. How do you identify errors in equations with fractions?

Tip: Always remember to find the least common denominator (LCD) when adding or subtracting fractions!