Solve v-10/2+v-8/4+v-10/5+v/2-10^-3+frac{v}{1}=0

$$\frac { v - 10 } { 2 } + \frac { v - 8 } { 4 } + \frac { v - 10 } { 5 } + \frac { v } { 2 } - 10 ^ { - 3 } + \frac { v } { 1 } = 0$$

Solve for v

$$v = \frac{9001}{2450} = 3\frac{1651}{2450} \approx 3.673877551$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 20, the least common multiple of 2,4,5.

$$20\left(\frac{v-10}{2}+\frac{v-8}{4}+\frac{v-10}{5}+\frac{v}{2}-10^{-3}\right)+20v=0$$

Combine \frac{v-10}{2} and \frac{v-10}{5} to get \frac{7}{10}\left(v-10\right).

$$20\left(\frac{7}{10}\left(v-10\right)+\frac{v-8}{4}+\frac{v}{2}-10^{-3}\right)+20v=0$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 2 is 4. Multiply \frac{v}{2} times \frac{2}{2}.

$$20\left(\frac{7}{10}\left(v-10\right)+\frac{v-8}{4}+\frac{2v}{4}-10^{-3}\right)+20v=0$$

Since \frac{v-8}{4} and \frac{2v}{4} have the same denominator, add them by adding their numerators.

$$20\left(\frac{7}{10}\left(v-10\right)+\frac{v-8+2v}{4}-10^{-3}\right)+20v=0$$

Combine like terms in v-8+2v.

$$20\left(\frac{7}{10}\left(v-10\right)+\frac{3v-8}{4}-10^{-3}\right)+20v=0$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$20\left(\frac{7}{10}\left(v-10\right)+\frac{3v-8}{4}-\frac{1}{1000}\right)+20v=0$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 1000 is 1000. Multiply \frac{3v-8}{4} times \frac{250}{250}.

$$20\left(\frac{7}{10}\left(v-10\right)+\frac{250\left(3v-8\right)}{1000}-\frac{1}{1000}\right)+20v=0$$

Since \frac{250\left(3v-8\right)}{1000} and \frac{1}{1000} have the same denominator, subtract them by subtracting their numerators.

$$20\left(\frac{7}{10}\left(v-10\right)+\frac{250\left(3v-8\right)-1}{1000}\right)+20v=0$$

Do the multiplications in 250\left(3v-8\right)-1.

$$20\left(\frac{7}{10}\left(v-10\right)+\frac{750v-2000-1}{1000}\right)+20v=0$$

Combine like terms in 750v-2000-1.

$$20\left(\frac{7}{10}\left(v-10\right)+\frac{750v-2001}{1000}\right)+20v=0$$

Use the distributive property to multiply 20 by \frac{7}{10}\left(v-10\right)+\frac{750v-2001}{1000}.

$$14v-140+20\times \frac{750v-2001}{1000}+20v=0$$

Cancel out 1000, the greatest common factor in 20 and 1000.

$$14v-140+\frac{750v-2001}{50}+20v=0$$

Combine 14v and 20v to get 34v.

$$34v-140+\frac{750v-2001}{50}=0$$

Divide each term of 750v-2001 by 50 to get 15v-\frac{2001}{50}.

$$34v-140+15v-\frac{2001}{50}=0$$

Combine 34v and 15v to get 49v.

$$49v-140-\frac{2001}{50}=0$$

Subtract \frac{2001}{50} from -140 to get -\frac{9001}{50}.

$$49v-\frac{9001}{50}=0$$

Add \frac{9001}{50} to both sides. Anything plus zero gives itself.

$$49v=\frac{9001}{50}$$

Divide both sides by 49.

$$v=\frac{\frac{9001}{50}}{49}$$

Express \frac{\frac{9001}{50}}{49} as a single fraction.

$$v=\frac{9001}{50\times 49}$$

Multiply 50 and 49 to get 2450.

$$v=\frac{9001}{2450}$$