`17(6x-50)=204((7)/(24)x)`
For what value of x is the equation above true?

Explanation

To solve the equation \( 17(6x - 50) = 204 \left(\frac{7}{24}x\right) \), we will follow these steps:

### Step 1: Simplify both sides of the equation
Start by distributing the 17 on the left side:
\[ 17(6x - 50) = 102x - 850 \]
Now, rewrite the equation:
\[ 102x - 850 = 204 \left(\frac{7}{24}x\right) \]

### Step 2: Simplify the right side
Calculate \( 204 \times \frac{7}{24} \):
\[ 204 \div 17 = 12 \quad \text{(since } 204 = 17 \times 12\text{)} \]
Now, simplify \( 12 \times 7 = 84 \):
\[ 204 \left(\frac{7}{24}x\right) = \frac{84}{24}x = \frac{7}{2}x \]
Now, the equation looks like this:
\[ 102x - 850 = \frac{7}{2}x \]

### Step 3: Eliminate the fraction
To eliminate the fraction, multiply the entire equation by 2:
\[ 2(102x - 850) = 2 \left(\frac{7}{2}x\right) \]
This gives:
\[ 204x - 1700 = 7x \]

### Step 4: Rearrange the equation
Now, move \( 7x \) to the left side:
\[ 204x - 7x = 1700 \]
This simplifies to:
\[ 197x = 1700 \]

### Step 5: Solve for \( x \)
Now, divide both sides by 197:
\[ x = \frac{1700}{197} \]

### Step 6: Calculate the value of \( x \)
Calculating \( \frac{1700}{197} \) gives approximately:
\[ x \approx 8.63 \]

### Final Answer
Thus, the value of \( x \) for which the equation is true is:
\[ x \approx 8.63 \]