Question

solve for ( v ):
( -\frac{3}{4} = \frac{5}{7}v - \frac{3}{2} )
simplify your answer as much as possible.

Explanation:

Step1: Add $\frac{3}{2}$ to both sides

To isolate the term with \( v \), we add \(\frac{3}{2}\) to both sides of the equation \(-\frac{3}{4}=\frac{5}{7}v - \frac{3}{2}\).

$$ -\frac{3}{4}+\frac{3}{2}=\frac{5}{7}v-\frac{3}{2}+\frac{3}{2} $$

Simplify the left - hand side: \(\frac{3}{2}-\frac{3}{4}=\frac{6 - 3}{4}=\frac{3}{4}\), and the right - hand side becomes \(\frac{5}{7}v\). So we have \(\frac{3}{4}=\frac{5}{7}v\).

Step2: Solve for \(v\) by multiplying both sides by \(\frac{7}{5}\)

To solve for \(v\), we multiply both sides of the equation \(\frac{3}{4}=\frac{5}{7}v\) by the reciprocal of \(\frac{5}{7}\), which is \(\frac{7}{5}\).

$$ v=\frac{3}{4}\times\frac{7}{5} $$

Multiply the numerators and denominators: \(v = \frac{3\times7}{4\times5}=\frac{21}{20}\)

Answer:

\(v=\frac{21}{20}\)