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Solve for [tex]\( x \)[/tex]:

[tex]\[ \frac{2}{v} = \frac{6}{7} \][/tex]

Give your answer as a common fraction.

Sagot :

GinnyAnswer
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]
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