The value of x for which the expression `19-5x` and 19x + 5 become equal is ____

Options

A. `7//12`
B. `-7//12`
C. `12//7`
D. `-12//7`

Answer

To find the value of \( x \) for which the expressions \( 19 - 5x \) and \( 19x + 5 \) are equal, we can set up the equation:

\[ 19 - 5x = 19x + 5 \]

### Step 1: Rearranging the equation
First, we will move all terms involving \( x \) to one side and constant terms to the other side.

\[ 19 - 5 = 19x + 5x \]

This simplifies to:

\[ 14 = 24x \]

### Step 2: Solving for \( x \)
Now, we will solve for \( x \) by dividing both sides of the equation by 24:

\[ x = \frac{14}{24} \]

### Step 3: Simplifying the fraction
Next, we simplify the fraction \( \frac{14}{24} \):

\[ x = \frac{14 \div 2}{24 \div 2} = \frac{7}{12} \]

### Final Answer
Thus, the value of \( x \) for which the expressions \( 19 - 5x \) and \( 19x + 5 \) are equal is:

\[ \boxed{\frac{7}{12}} \]

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