https://file.aiquickdraw.com/mathbot/file/1727215137029np5xm8ad.jpg

Let's break down and solve the equation visible in the image.

The equation is:

\[
- 2 \frac{1}{10} - \left( - \frac{7}{10} \right) = -1 \frac{1}{2}
\]

### Step-by-step solution:

1. **Convert Mixed Numbers to Improper Fractions**:
   - \( - 2 \frac{1}{10} \) becomes \( - \frac{21}{10} \) (because \( -2 \frac{1}{10} = -\left(\frac{20}{10} + \frac{1}{10}\right) = -\frac{21}{10} \)).
   - \( -1 \frac{1}{2} \) becomes \( - \frac{3}{2} \).

   Now the equation looks like:

   \[
   - \frac{21}{10} - \left( - \frac{7}{10} \right) = - \frac{3}{2}
   \]

2. **Simplify**:
   - The negative sign outside the parentheses becomes positive: 
   
   \[
   - \frac{21}{10} + \frac{7}{10} = - \frac{3}{2}
   \]
   
   Combine the fractions on the left-hand side:

   \[
   \frac{-21 + 7}{10} = - \frac{14}{10}
   \]
   
   Simplify \( - \frac{14}{10} \) to \( - \frac{7}{5} \).

3. **Equate and Simplify**:
   Now the equation is:

   \[
   - \frac{7}{5} = - \frac{3}{2}
   \]

   To check equality, we can cross-multiply:
   
   \[
   -7 \times 2 = -5 \times 3
   \]

   Which simplifies to:

   \[
   -14 = -15
   \]

   This is false, meaning the equation as given does not hold true. Therefore, there seems to be an error in the original equation, or we need to recheck the steps.

Would you like any further details on these steps or want to discuss another question from this exercise?

### 5 Related Questions:
1. How do you convert a mixed number into an improper fraction?
2. How do you combine fractions with different denominators?
3. What steps should you follow to simplify complex fractions?
4. How can you check if two fractions are equal using cross-multiplication?
5. What are common errors in solving equations with mixed numbers?

**Tip**: Always simplify fractions as much as possible to make comparisons easier.

Learn how to solve the equation -2 1/10 - (-7/10) = -1 1/2 by converting mixed numbers to improper fractions and performing operations on fractions with like denominators. Suitable for students in Grades 6-8.

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