Solve 4/3v-2/3=-3v-3/4

$$\frac { 4 } { 3 } v - \frac { 2 } { 3 } = - 3 v - \frac { 3 } { 4 }$$

Solve for v

$$v=-\frac{1}{52}\approx -0.019230769$$

Steps for Solving Linear Equation

Add 3v to both sides.

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

Combine \frac{4}{3}v and 3v to get \frac{13}{3}v.

$$\frac{13}{3}v-\frac{2}{3}=-\frac{3}{4}$$

Add \frac{2}{3} to both sides.

$$\frac{13}{3}v=-\frac{3}{4}+\frac{2}{3}$$

Least common multiple of 4 and 3 is 12. Convert -\frac{3}{4} and \frac{2}{3} to fractions with denominator 12.

$$\frac{13}{3}v=-\frac{9}{12}+\frac{8}{12}$$

Since -\frac{9}{12} and \frac{8}{12} have the same denominator, add them by adding their numerators.

$$\frac{13}{3}v=\frac{-9+8}{12}$$

Add -9 and 8 to get -1.

$$\frac{13}{3}v=-\frac{1}{12}$$

Multiply both sides by \frac{3}{13}, the reciprocal of \frac{13}{3}.

$$v=-\frac{1}{12}\times \frac{3}{13}$$

Multiply -\frac{1}{12} times \frac{3}{13} by multiplying numerator times numerator and denominator times denominator.

$$v=\frac{-3}{12\times 13}$$

Do the multiplications in the fraction \frac{-3}{12\times 13}.

$$v=\frac{-3}{156}$$

Reduce the fraction \frac{-3}{156} to lowest terms by extracting and canceling out 3.

$$v=-\frac{1}{52}$$