`2(1)/(4)+3(3)/(5)=? -4(3)/(10)`

Options

A. `9(7)/(10)`
B. `7(7)/(10)`
C. `9(3)/(10)`
D. None of these

Explanation

To solve the equation \( 2\frac{1}{4} + 3\frac{3}{5} = ? - 4\frac{3}{10} \), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert the mixed numbers into improper fractions.

1. For \( 2\frac{1}{4} \):
\[ 2\frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{8 + 1}{4} = \frac{9}{4} \]

2. For \( 3\frac{3}{5} \):
\[ 3\frac{3}{5} = \frac{3 \times 5 + 3}{5} = \frac{15 + 3}{5} = \frac{18}{5} \]

3. For \( 4\frac{3}{10} \):
\[ 4\frac{3}{10} = \frac{4 \times 10 + 3}{10} = \frac{40 + 3}{10} = \frac{43}{10} \]

### Step 2: Set Up the Equation
Now we can rewrite the equation using improper fractions:
\[ \frac{9}{4} + \frac{18}{5} = x - \frac{43}{10} \]

### Step 3: Isolate \( x \)
To find \( x \), we can rearrange the equation:
\[ x = \frac{9}{4} + \frac{18}{5} + \frac{43}{10} \]

### Step 4: Find a Common Denominator
The least common multiple (LCM) of the denominators \( 4, 5, \) and \( 10 \) is \( 20 \).

### Step 5: Convert Each Fraction
Now we convert each fraction to have a denominator of \( 20 \):

1. Convert \( \frac{9}{4} \):
\[ \frac{9}{4} = \frac{9 \times 5}{4 \times 5} = \frac{45}{20} \]

2. Convert \( \frac{18}{5} \):
\[ \frac{18}{5} = \frac{18 \times 4}{5 \times 4} = \frac{72}{20} \]

3. Convert \( \frac{43}{10} \):
\[ \frac{43}{10} = \frac{43 \times 2}{10 \times 2} = \frac{86}{20} \]

### Step 6: Add the Fractions
Now we can add the fractions:
\[ x = \frac{45}{20} + \frac{72}{20} + \frac{86}{20} = \frac{45 + 72 + 86}{20} = \frac{203}{20} \]

### Step 7: Simplify the Result
Now, we can simplify \( \frac{203}{20} \):
\[ x = 10.15 \]

### Final Answer
Thus, the value of \( x \) is:
\[ \boxed{10.15} \]