Solve -7/4v+5/2=-6v-2/3

$$- \frac { 7 } { 4 } v + \frac { 5 } { 2 } = - 6 v - \frac { 2 } { 3 }$$

Solve for v

$$v=-\frac{38}{51}\approx -0.745098039$$

Steps for Solving Linear Equation

Add 6v to both sides.

$$-\frac{7}{4}v+\frac{5}{2}+6v=-\frac{2}{3}$$

Combine -\frac{7}{4}v and 6v to get \frac{17}{4}v.

$$\frac{17}{4}v+\frac{5}{2}=-\frac{2}{3}$$

Subtract \frac{5}{2} from both sides.

$$\frac{17}{4}v=-\frac{2}{3}-\frac{5}{2}$$

Least common multiple of 3 and 2 is 6. Convert -\frac{2}{3} and \frac{5}{2} to fractions with denominator 6.

$$\frac{17}{4}v=-\frac{4}{6}-\frac{15}{6}$$

Since -\frac{4}{6} and \frac{15}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{17}{4}v=\frac{-4-15}{6}$$

Subtract 15 from -4 to get -19.

$$\frac{17}{4}v=-\frac{19}{6}$$

Multiply both sides by \frac{4}{17}, the reciprocal of \frac{17}{4}.

$$v=-\frac{19}{6}\times \frac{4}{17}$$

Multiply -\frac{19}{6} times \frac{4}{17} by multiplying numerator times numerator and denominator times denominator.

$$v=\frac{-19\times 4}{6\times 17}$$

Do the multiplications in the fraction \frac{-19\times 4}{6\times 17}.

$$v=\frac{-76}{102}$$

Reduce the fraction \frac{-76}{102} to lowest terms by extracting and canceling out 2.

$$v=-\frac{38}{51}$$