To find the value of [tex]\( x \)[/tex] in the rational equation [tex]\(\frac{8}{2x} = \frac{12}{15}\)[/tex], follow these steps:
1. Write down the given equation:
[tex]\[
\frac{8}{2x} = \frac{12}{15}
\][/tex]
2. Cross-multiply to eliminate the fractions:
[tex]\[
8 \times 15 = 12 \times 2x
\][/tex]
3. Calculate the products on both sides:
[tex]\[
120 = 24x
\][/tex]
4. Solve for [tex]\( x \)[/tex] by isolating it on one side of the equation. To do this, divide both sides by 24:
[tex]\[
x = \frac{120}{24}
\][/tex]
5. Simplify the fraction:
[tex]\[
x = 5
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is [tex]\( 5 \)[/tex].
The correct answer is:
[tex]\[ 5 \][/tex]
