Question

solve for v.
\\(\frac{3}{4} = \frac{v - 4}{10}\\)
simplify your answer as much as possible.
\\(v = \square\\)

Explanation:

Step1: Cross - multiply to eliminate fractions

To solve the equation \(\frac{3}{4}=\frac{v - 4}{10}\), we cross - multiply. Cross - multiplying gives us \(3\times10 = 4\times(v - 4)\).
So, \(30=4(v - 4)\).

Step2: Distribute the 4 on the right - hand side

Using the distributive property \(a(b - c)=ab - ac\), where \(a = 4\), \(b = v\) and \(c = 4\), we get \(30 = 4v-16\).

Step3: Add 16 to both sides of the equation

To isolate the term with \(v\), we add 16 to both sides of the equation.
\(30 + 16=4v-16 + 16\).
Simplifying the left - hand side and the right - hand side, we have \(46 = 4v\).

Step4: Solve for v by dividing both sides by 4

Divide both sides of the equation \(46 = 4v\) by 4.
\(v=\frac{46}{4}\), and simplifying the fraction \(\frac{46}{4}\) (dividing numerator and denominator by 2), we get \(v=\frac{23}{2}=11.5\).

Answer:

\(v = \frac{23}{2}\) (or \(v = 11.5\))