If `7sqrt(x)-24=11,` what is the value of x?

Options

A. `sqrt(5)`
B. `sqrt(7)`
C. `5`
D. `25`

Answer

To solve the equation \( 7\sqrt{x} - 24 = 11 \), we can follow these steps:

### Step 1: Isolate the square root term
We start by moving the constant term (-24) to the right side of the equation:

\[ 7\sqrt{x} = 11 + 24 \]

### Step 2: Simplify the right side
Now, we calculate the right side:

\[ 7\sqrt{x} = 35 \]

### Step 3: Divide both sides by 7
Next, we divide both sides of the equation by 7 to solve for \(\sqrt{x}\):

\[ \sqrt{x} = \frac{35}{7} \]

### Step 4: Calculate the division
Now we perform the division:

\[ \sqrt{x} = 5 \]

### Step 5: Square both sides
To eliminate the square root, we square both sides of the equation:

\[ (\sqrt{x})^2 = 5^2 \]

### Step 6: Simplify the squares
This gives us:

\[ x = 25 \]

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

\[ \boxed{25} \]