https://file.aiquickdraw.com/mathbot/file/1726448391404l2dh1avp.jpg

The equation you need to solve is:

\[
r - 2 = \frac{-2}{5} + \frac{7}{10} + \frac{3}{2}
\]

Let's solve this step-by-step.

### Step 1: Simplify the right-hand side
We need to combine the fractions on the right-hand side. To do this, we find the least common denominator (LCD) of the fractions.

- The denominators are 5, 10, and 2.
- The LCD of 5, 10, and 2 is 10.

Now, rewrite each fraction with the denominator of 10:
\[
\frac{-2}{5} = \frac{-4}{10}, \quad \frac{7}{10} = \frac{7}{10}, \quad \frac{3}{2} = \frac{15}{10}
\]

### Step 2: Add the fractions
Now, add the fractions:
\[
\frac{-4}{10} + \frac{7}{10} + \frac{15}{10} = \frac{-4 + 7 + 15}{10} = \frac{18}{10}
\]
Simplify \(\frac{18}{10}\):
\[
\frac{18}{10} = 1.8
\]

### Step 3: Solve for \( r \)
Now, substitute the simplified value back into the equation:
\[
r - 2 = 1.8
\]

Add 2 to both sides:
\[
r = 1.8 + 2 = 3.8
\]

Thus, the solution is:
\[
r = 3.8
\]

Would you like more details or have any questions about this process?

### Related Questions:
1. How do you find the least common denominator of fractions?
2. How can you simplify fractions like \(\frac{18}{10}\)?
3. What are some methods to solve linear equations with fractions?
4. How can you check your solution to a linear equation?
5. What happens if you have variables on both sides of the equation?

**Tip**: Always simplify fractions before adding or subtracting them to avoid errors.

Solve for r: r - 2 = (-2/5) + (7/10) + (3/2)

Learn how to solve a linear equation involving fractions. This example covers algebraic concepts, including finding the least common denominator and combining fractions. Suitable for students in Grades 8-10.

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