If `(5x)/3-4=(2x)/5` then find the numerical value of 2x – 7.

Options

A. `19/13`
B. `-13/19`
C. 0
D. `13/19`

Answer

To solve the equation \(\frac{5x}{3} - 4 = \frac{2x}{5}\) and find the numerical value of \(2x - 7\), we will follow these steps:

### Step 1: Eliminate the fractions
To eliminate the fractions, we can find a common denominator. The least common multiple of 3 and 5 is 15. We will multiply every term in the equation by 15:

\[ 15 \left(\frac{5x}{3}\right) - 15(4) = 15 \left(\frac{2x}{5}\right) \]

This simplifies to:

\[ 5 \cdot 5x - 60 = 3 \cdot 2x \]

### Step 2: Simplify the equation
Now we simplify the equation:

\[ 25x - 60 = 6x \]

### Step 3: Move all terms involving \(x\) to one side
Next, we will move \(6x\) to the left side of the equation:

\[ 25x - 6x - 60 = 0 \]

This simplifies to:

\[ 19x - 60 = 0 \]

### Step 4: Solve for \(x\)
Now, we will isolate \(x\) by adding 60 to both sides:

\[ 19x = 60 \]

Next, divide both sides by 19:

\[ x = \frac{60}{19} \]

### Step 5: Find \(2x - 7\)
Now we need to find the value of \(2x - 7\):

\[ 2x - 7 = 2\left(\frac{60}{19}\right) - 7 \]

This simplifies to:

\[ = \frac{120}{19} - 7 \]

### Step 6: Convert 7 to a fraction with a denominator of 19
To subtract, we convert 7 into a fraction:

\[ 7 = \frac{133}{19} \]

Now we can subtract:

\[ 2x - 7 = \frac{120}{19} - \frac{133}{19} = \frac{120 - 133}{19} = \frac{-13}{19} \]

### Final Answer
Thus, the numerical value of \(2x - 7\) is:

\[ \boxed{\frac{-13}{19}} \]