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

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

Solve for v

$$v = -\frac{25}{14} = -1\frac{11}{14} \approx -1.785714286$$

Steps for Solving Linear Equation

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

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

Add \frac{1}{7} to both sides.

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

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

$$\frac{1}{5}v=-\frac{7}{14}+\frac{2}{14}$$

Since -\frac{7}{14} and \frac{2}{14} have the same denominator, add them by adding their numerators.

$$\frac{1}{5}v=\frac{-7+2}{14}$$

Add -7 and 2 to get -5.

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

Multiply both sides by 5, the reciprocal of \frac{1}{5}.

$$v=-\frac{5}{14}\times 5$$

Express -\frac{5}{14}\times 5 as a single fraction.

$$v=\frac{-5\times 5}{14}$$

Multiply -5 and 5 to get -25.

$$v=\frac{-25}{14}$$

Fraction \frac{-25}{14} can be rewritten as -\frac{25}{14} by extracting the negative sign.

$$v=-\frac{25}{14}$$