Find the value of `x`
`-2(1)/(3)+4(3)/(5)`= `x`

Options

A. `1(1)/(21)`
B. `(5)/(21)`
C. `(-5)/(21)`
D. none

Answer

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

### Step 1: Convert Mixed Numbers to Improper Fractions
1. Convert \(-2\frac{1}{3}\) to an improper fraction:
\[ -2\frac{1}{3} = -\left(2 \times 3 + 1\right)/3 = -\frac{6 + 1}{3} = -\frac{7}{3} \]

2. Convert \(4\frac{3}{5}\) to an improper fraction:
\[ 4\frac{3}{5} = \left(4 \times 5 + 3\right)/5 = \frac{20 + 3}{5} = \frac{23}{5} \]

### Step 2: Add the Improper Fractions
Now we need to add \(-\frac{7}{3}\) and \(\frac{23}{5}\). To do this, we need a common denominator.

1. The least common multiple (LCM) of 3 and 5 is 15.
2. Convert \(-\frac{7}{3}\) to a fraction with a denominator of 15:
\[ -\frac{7}{3} = -\frac{7 \times 5}{3 \times 5} = -\frac{35}{15} \]

3. Convert \(\frac{23}{5}\) to a fraction with a denominator of 15:
\[ \frac{23}{5} = \frac{23 \times 3}{5 \times 3} = \frac{69}{15} \]

### Step 3: Combine the Fractions
Now we can add the two fractions:
\[ -\frac{35}{15} + \frac{69}{15} = \frac{-35 + 69}{15} = \frac{34}{15} \]

### Step 4: Write the Final Answer
Thus, the value of \(x\) is:
\[ x = \frac{34}{15} \]

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