To solve the equation \( \frac{3.5}{1.2x} = 5.4 \) for the variable \( x \), we can follow these steps:
Step 1: Isolate the fraction
We start with the original equation:
\[ \frac{3.5}{1.2x} = 5.4 \]
Step 2: Eliminate the fraction
To eliminate the fraction, multiply both sides by \( 1.2x \):
\[ 3.5 = 5.4 \cdot (1.2x) \]
Step 3: Distribute on the right side
Next, distribute \( 5.4 \) on the right side:
\[ 3.5 = 5.4 \cdot 1.2 \cdot x \]
Step 4: Calculate \( 5.4 \cdot 1.2 \)
Now we calculate \( 5.4 \cdot 1.2 \):
\[ 5.4 \cdot 1.2 = 6.48 \]
So the equation now looks like this:
\[ 3.5 = 6.48x \]
Step 5: Solve for \( x \)
To isolate \( x \), divide both sides by \( 6.48 \):
\[ x = \frac{3.5}{6.48} \]
Step 6: Calculate the value of \( x \)
Now we perform the division:
\[ x = \frac{3.5}{6.48} \approx 0.54 \]
Thus, the solution to the equation \( \frac{3.5}{1.2x} = 5.4 \) is:
\[ \boxed{0.54} \]