Solve the equations and check your answer in the case:
`x-24%` of `x=38`

Answer

To solve the equation \( x - 24\% \text{ of } x = 38 \), we will follow these steps:

### Step 1: Convert the percentage to a fraction
First, we need to express 24% as a fraction.
\[ 24\% = \frac{24}{100} \]

### Step 2: Rewrite the equation
Now, we can rewrite the equation using the fraction:
\[ x - \frac{24}{100}x = 38 \]

### Step 3: Combine like terms
To combine the terms on the left side, we can factor \( x \):
\[ x - \frac{24}{100}x = \left(1 - \frac{24}{100}\right)x = \frac{100}{100}x - \frac{24}{100}x = \frac{76}{100}x \]
So, the equation becomes:
\[ \frac{76}{100}x = 38 \]

### Step 4: Eliminate the fraction
To eliminate the fraction, we can multiply both sides of the equation by 100:
\[ 76x = 38 \times 100 \]
Calculating the right side:
\[ 76x = 3800 \]

### Step 5: Solve for \( x \)
Now, divide both sides by 76 to find \( x \):
\[ x = \frac{3800}{76} \]
Calculating this gives:
\[ x = 50 \]

### Step 6: Verify the solution
To verify, we substitute \( x = 50 \) back into the original equation:
\[ 50 - 24\% \text{ of } 50 = 38 \]
Calculating \( 24\% \text{ of } 50 \):
\[ 24\% \text{ of } 50 = \frac{24}{100} \times 50 = 12 \]
Now substituting back:
\[ 50 - 12 = 38 \]
This confirms that our solution is correct since both sides are equal.

### Final Answer
Thus, the solution to the equation is:
\[ \boxed{50} \]