To solve the equation [tex]\( \frac{9}{2x} = \frac{3}{4} \)[/tex], follow these steps:
1. Cross-multiply to eliminate the fractions:
Multiply both sides of the equation by [tex]\( 2x \)[/tex] and 4 to get rid of the denominators. This results in:
[tex]\[
9 \cdot 4 = 3 \cdot 2x
\][/tex]
2. Simplify the equation:
Calculate the products on both sides:
[tex]\[
36 = 6x
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
Divide both sides of the equation by 6 to isolate [tex]\( x \)[/tex]:
[tex]\[
x = \frac{36}{6}
\][/tex]
4. Simplify the division:
[tex]\[
x = 6
\][/tex]
Thus, the solution to the equation [tex]\( \frac{9}{2x} = \frac{3}{4} \)[/tex] is [tex]\( \boxed{6} \)[/tex].
