Solve 1/7-3/2v=4/5

$$\frac { 1 } { 7 } - \frac { 3 } { 2 } v = \frac { 4 } { 5 }$$

Solve for v

$$v=-\frac{46}{105}\approx -0.438095238$$

Steps for Solving Linear Equation

Subtract \frac{1}{7} from both sides.

$$-\frac{3}{2}v=\frac{4}{5}-\frac{1}{7}$$

Least common multiple of 5 and 7 is 35. Convert \frac{4}{5} and \frac{1}{7} to fractions with denominator 35.

$$-\frac{3}{2}v=\frac{28}{35}-\frac{5}{35}$$

Since \frac{28}{35} and \frac{5}{35} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{3}{2}v=\frac{28-5}{35}$$

Subtract 5 from 28 to get 23.

$$-\frac{3}{2}v=\frac{23}{35}$$

Multiply both sides by -\frac{2}{3}, the reciprocal of -\frac{3}{2}.

$$v=\frac{23}{35}\left(-\frac{2}{3}\right)$$

Multiply \frac{23}{35} times -\frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$v=\frac{23\left(-2\right)}{35\times 3}$$

Do the multiplications in the fraction \frac{23\left(-2\right)}{35\times 3}.

$$v=\frac{-46}{105}$$

Fraction \frac{-46}{105} can be rewritten as -\frac{46}{105} by extracting the negative sign.

$$v=-\frac{46}{105}$$