To solve the equation \( \frac{5}{9} (x - 3) = \frac{8}{25} \), follow these steps:
-
Eliminate the fraction by multiplying both sides by the least common multiple (LCM) of the denominators. The denominators are 9 and 25, and their LCM is 225. Multiply both sides by 225:
\[ 225 \cdot \frac{5}{9} (x - 3) = 225 \cdot \frac{8}{25} \]
-
Calculate each side:
\[ 225 \cdot \frac{5}{9} = 25 \cdot 5 = 125 \]
\[ 225 \cdot \frac{8}{25} = 9 \cdot 8 = 72 \]
So, we have:
\[ 125(x - 3) = 72 \]
-
Distribute on the left side:
\[ 125x - 375 = 72 \]
-
Add 375 to both sides to isolate the term with \(x\):
\[ 125x = 72 + 375 \] \[ 125x = 447 \]
-
Divide both sides by 125 to solve for \(x\):
\[ x = \frac{447}{125} \]
Thus, the solution to the equation \( \frac{5}{9} (x - 3) = \frac{8}{25} \) is:
\[ x = \frac{447}{125} \]