What is the value of x, if `(5+4^(2)) div 3 " of "1/ x- 2 xx 4= -7` ?

Options

A. `-3`
B. 5
C. 7
D. `-7`

Answer

To solve the equation \( (5 + 4^2) \div 3 \cdot \frac{1}{x} - 2 \cdot 4 = -7 \), let's break it down step by step.

### Step 1: Simplify \( 4^2 \)
Calculate \( 4^2 \):
\[ 4^2 = 16 \]
So, we rewrite the equation:
\[ (5 + 16) \div 3 \cdot \frac{1}{x} - 2 \cdot 4 = -7 \]

### Step 2: Add \( 5 + 16 \)
Now, add \( 5 \) and \( 16 \):
\[ 5 + 16 = 21 \]
The equation now looks like:
\[ 21 \div 3 \cdot \frac{1}{x} - 2 \cdot 4 = -7 \]

### Step 3: Divide \( 21 \) by \( 3 \)
Next, divide \( 21 \) by \( 3 \):
\[ 21 \div 3 = 7 \]
The equation simplifies to:
\[ 7 \cdot \frac{1}{x} - 2 \cdot 4 = -7 \]

### Step 4: Calculate \( 2 \cdot 4 \)
Now, calculate \( 2 \cdot 4 \):
\[ 2 \cdot 4 = 8 \]
So, the equation becomes:
\[ 7 \cdot \frac{1}{x} - 8 = -7 \]

### Step 5: Add \( 8 \) to both sides
Add \( 8 \) to both sides of the equation:
\[ 7 \cdot \frac{1}{x} = -7 + 8 \]
This simplifies to:
\[ 7 \cdot \frac{1}{x} = 1 \]

### Step 6: Isolate \( \frac{1}{x} \)
Now, isolate \( \frac{1}{x} \) by dividing both sides by \( 7 \):
\[ \frac{1}{x} = \frac{1}{7} \]

### Step 7: Solve for \( x \)
Take the reciprocal of both sides to solve for \( x \):
\[ x = 7 \]

### Final Answer
Thus, the value of \( x \) is:
\[ \boxed{7} \]