Solve.
\[
\frac{10}{63} x-\frac{9}{7}=\frac{10}{9}+\frac{9}{21} x
\]
$x=$
(Simplify your answer.)
The solution to the equation is \(x = \boxed{-0.0201413898892891}\).
Step 1 :First, we need to get rid of the fractions in the equation \(\frac{10}{63} x-\frac{9}{7}=\frac{10}{9}+\frac{9}{21} x\). We can do this by multiplying every term by the least common multiple (LCM) of the denominators (63, 7, 9, 21). The LCM of these numbers is 441.
Step 2 :After multiplying each term by 441, the equation becomes \(70.0x - 1.28571428571429 = 189.0x + 1.11111111111111\).
Step 3 :Next, we simplify the equation and solve for x.
Step 4 :The solution to the equation is \(x = \boxed{-0.0201413898892891}\).