Sure, let's solve for [tex]\( v \)[/tex] in the equation [tex]\(\frac{2}{v} = \frac{6}{7}\)[/tex].
1. Start with the given equation:
[tex]\[
\frac{2}{v} = \frac{6}{7}
\][/tex]
2. To clear the fraction, we can cross-multiply. This gives us:
[tex]\[
2 \cdot 7 = 6 \cdot v
\][/tex]
3. Simplify the products on each side:
[tex]\[
14 = 6v
\][/tex]
4. To isolate [tex]\( v \)[/tex], divide both sides of the equation by 6:
[tex]\[
v = \frac{14}{6}
\][/tex]
5. Simplify the fraction by dividing the numerator and the denominator by their greatest common divisor, which is 2:
[tex]\[
v = \frac{14 \div 2}{6 \div 2} = \frac{7}{3}
\][/tex]
Therefore, the solution for [tex]\( v \)[/tex] as a common fraction is:
[tex]\[
v = \frac{7}{3}
\][/tex]
