Question

linear equations and inequalities
solving a two - step equation with signed fractions
solve for v.
$-\frac{5}{2}+\frac{4}{3}v = -\frac{8}{5}$
simplify your answer as much as possible.
$v=square$

Explanation:

Step1: Add $\frac{5}{2}$ to both sides

To isolate the term with \( v \), we add \(\frac{5}{2}\) to both sides of the equation \(-\frac{5}{2}+\frac{4}{3}v = -\frac{8}{5}\). This gives us \(\frac{4}{3}v=-\frac{8}{5}+\frac{5}{2}\).
To add the fractions on the right - hand side, we find a common denominator. The common denominator of 5 and 2 is 10. So, \(-\frac{8}{5}=-\frac{8\times2}{5\times2}=-\frac{16}{10}\) and \(\frac{5}{2}=\frac{5\times5}{2\times5}=\frac{25}{10}\). Then \(-\frac{8}{5}+\frac{5}{2}=-\frac{16}{10}+\frac{25}{10}=\frac{- 16 + 25}{10}=\frac{9}{10}\). So now our equation is \(\frac{4}{3}v=\frac{9}{10}\).

Step2: Solve for \(v\)

To solve for \(v\), we multiply both sides of the equation \(\frac{4}{3}v=\frac{9}{10}\) by the reciprocal of \(\frac{4}{3}\), which is \(\frac{3}{4}\). So \(v=\frac{9}{10}\times\frac{3}{4}\).
When we multiply two fractions, we multiply the numerators together and the denominators together. So \(v = \frac{9\times3}{10\times4}=\frac{27}{40}\).

Answer:

\(v=\frac{27}{40}\)