Find the value of x in the following expression
`5(5x-4)= 16 (5x+1)`

Options

A. `(4)/(5)`
B. `(-36)/(55)`
C. `(5)/(4)`
D. `(-55)/(44)`

Answer

To solve the equation \( 5(5x - 4) = 16(5x + 1) \), we will follow these steps:

### Step 1: Expand both sides of the equation
Start by distributing the numbers outside the parentheses on both sides.

\[ 5(5x - 4) = 5 \cdot 5x - 5 \cdot 4 = 25x - 20 \]

\[ 16(5x + 1) = 16 \cdot 5x + 16 \cdot 1 = 80x + 16 \]

Now, we can rewrite the equation as:

\[ 25x - 20 = 80x + 16 \]

### Step 2: Rearrange the equation
Next, we will move all terms involving \( x \) to one side and constant terms to the other side.

Subtract \( 80x \) from both sides:

\[ 25x - 80x - 20 = 16 \]

This simplifies to:

\[ -55x - 20 = 16 \]

Now, add 20 to both sides:

\[ -55x = 16 + 20 \]

This simplifies to:

\[ -55x = 36 \]

### Step 3: Solve for \( x \)
Now, divide both sides by -55 to isolate \( x \):

\[ x = \frac{36}{-55} \]

This can be rewritten as:

\[ x = -\frac{36}{55} \]

### Final Answer
Thus, the value of \( x \) is:

\[ x = -\frac{36}{55} \]

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