Question

solve for v: \\(\frac{4}{3} = \frac{16}{v + 6}\\) (make sure to start your answer with \v=\ ) make sure you use the correct uppercase and lower case letters

Explanation:

Step1: Cross - multiply the fractions

To solve the equation \(\frac{4}{3}=\frac{16}{v + 6}\), we use the cross - multiplication property of proportions. If \(\frac{a}{b}=\frac{c}{d}\), then \(a\times d=b\times c\). So, we have \(4\times(v + 6)=3\times16\).

Step2: Simplify both sides of the equation

First, simplify the left - hand side: \(4(v + 6)=4v+24\), and the right - hand side: \(3\times16 = 48\). So our equation becomes \(4v+24 = 48\).

Step3: Subtract 24 from both sides

Subtract 24 from each side of the equation \(4v+24 = 48\) to isolate the term with \(v\). We get \(4v+24-24=48 - 24\), which simplifies to \(4v=24\).

Step4: Divide both sides by 4

Divide both sides of the equation \(4v = 24\) by 4. \(\frac{4v}{4}=\frac{24}{4}\), so \(v = 6\).

Answer:

\(v = 6\)