Solve frac{v_{0}-3}{1m}+7/47k=0

$$\frac { v _ { 0 } - 3 } { 1 m } + \frac { 7 } { 47 k } = 0$$

Solve for k

$$k=-\frac{7m}{47\left(v_{0}-3\right)}$$

$$m\neq 0\text{ and }v_{0}\neq 3$$

Steps for Solving Linear Equation

Variable k cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 47km, the least common multiple of 1m,47k.

$$47k\left(v_{0}-3\right)+m\times 7=0$$

Use the distributive property to multiply 47k by v_{0}-3.

$$47kv_{0}-141k+m\times 7=0$$

Subtract m\times 7 from both sides. Anything subtracted from zero gives its negation.

$$47kv_{0}-141k=-m\times 7$$

Multiply -1 and 7 to get -7.

$$47kv_{0}-141k=-7m$$

Combine all terms containing k.

$$\left(47v_{0}-141\right)k=-7m$$

Divide both sides by 47v_{0}-141.

$$\frac{\left(47v_{0}-141\right)k}{47v_{0}-141}=-\frac{7m}{47v_{0}-141}$$

Dividing by 47v_{0}-141 undoes the multiplication by 47v_{0}-141.

$$k=-\frac{7m}{47v_{0}-141}$$

Divide -7m by 47v_{0}-141.

$$k=-\frac{7m}{47\left(v_{0}-3\right)}$$

Variable k cannot be equal to 0.

$$k=-\frac{7m}{47\left(v_{0}-3\right)}\text{, }k\neq 0$$

Solve for m

$$m=-\frac{47k\left(v_{0}-3\right)}{7}$$

$$v_{0}\neq 3\text{ and }k\neq 0$$

Steps for Solving Linear Equation

Variable m cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 47km, the least common multiple of 1m,47k.

$$47k\left(v_{0}-3\right)+m\times 7=0$$

Use the distributive property to multiply 47k by v_{0}-3.

$$47kv_{0}-141k+m\times 7=0$$

Subtract 47kv_{0} from both sides. Anything subtracted from zero gives its negation.

$$-141k+m\times 7=-47kv_{0}$$

Add 141k to both sides.

$$m\times 7=-47kv_{0}+141k$$

The equation is in standard form.

$$7m=141k-47kv_{0}$$

Divide both sides by 7.

$$\frac{7m}{7}=\frac{47k\left(3-v_{0}\right)}{7}$$

Dividing by 7 undoes the multiplication by 7.

$$m=\frac{47k\left(3-v_{0}\right)}{7}$$

Variable m cannot be equal to 0.

$$m=\frac{47k\left(3-v_{0}\right)}{7}\text{, }m\neq 0$$