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

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

Solve for v

$$v=\frac{5}{28}\approx 0.178571429$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

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

Add \frac{4}{7} to both sides.

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

Least common multiple of 2 and 7 is 14. Convert -\frac{1}{2} and \frac{4}{7} to fractions with denominator 14.

$$\frac{2}{5}v=-\frac{7}{14}+\frac{8}{14}$$

Since -\frac{7}{14} and \frac{8}{14} have the same denominator, add them by adding their numerators.

$$\frac{2}{5}v=\frac{-7+8}{14}$$

Add -7 and 8 to get 1.

$$\frac{2}{5}v=\frac{1}{14}$$

Multiply both sides by \frac{5}{2}, the reciprocal of \frac{2}{5}.

$$v=\frac{1}{14}\times \frac{5}{2}$$

Multiply \frac{1}{14} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$v=\frac{1\times 5}{14\times 2}$$

Do the multiplications in the fraction \frac{1\times 5}{14\times 2}.

$$v=\frac{5}{28}$$