Solve v=1/2u+5*4/t

$$v = \frac { 1 } { 2 } u + 5 \cdot \frac { 4 } { t }$$

Solve for t

$$t=-\frac{40}{u-2v}$$

$$v\neq \frac{u}{2}$$

Steps for Solving Linear Equation

Variable t cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2t, the least common multiple of 2,t.

$$v\times 2t=\frac{1}{2}u\times 2t+5\times 2\times 4$$

Multiply \frac{1}{2} and 2 to get 1.

$$v\times 2t=ut+5\times 2\times 4$$

Multiply 5 and 2 to get 10.

$$v\times 2t=ut+10\times 4$$

Multiply 10 and 4 to get 40.

$$v\times 2t=ut+40$$

Subtract ut from both sides.

$$v\times 2t-ut=40$$

Combine all terms containing t.

$$\left(v\times 2-u\right)t=40$$

The equation is in standard form.

$$\left(2v-u\right)t=40$$

Divide both sides by 2v-u.

$$\frac{\left(2v-u\right)t}{2v-u}=\frac{40}{2v-u}$$

Dividing by 2v-u undoes the multiplication by 2v-u.

$$t=\frac{40}{2v-u}$$

Variable t cannot be equal to 0.

$$t=\frac{40}{2v-u}\text{, }t\neq 0$$

Solve for u

$$u=2v-\frac{40}{t}$$

$$t\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2t, the least common multiple of 2,t.

$$v\times 2t=\frac{1}{2}u\times 2t+5\times 2\times 4$$

Multiply \frac{1}{2} and 2 to get 1.

$$v\times 2t=ut+5\times 2\times 4$$

Multiply 5 and 2 to get 10.

$$v\times 2t=ut+10\times 4$$

Multiply 10 and 4 to get 40.

$$v\times 2t=ut+40$$

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

$$ut+40=v\times 2t$$

Subtract 40 from both sides.

$$ut=v\times 2t-40$$

The equation is in standard form.

$$tu=2tv-40$$

Divide both sides by t.

$$\frac{tu}{t}=\frac{2tv-40}{t}$$

Dividing by t undoes the multiplication by t.

$$u=\frac{2tv-40}{t}$$

Divide 2vt-40 by t.

$$u=2v-\frac{40}{t}$$