Solve 4.085-3.353/6-n=3.353-3.214/n-5

$$\frac { 4.085 - 3.353 } { 6 - n } = \frac { 3.353 - 3.214 } { n - 5 }$$

Solve for n

$$n = \frac{4494}{871} = 5\frac{139}{871} \approx 5.159586682$$

Steps for Solving Linear Equation

Variable n cannot be equal to any of the values 5,6 since division by zero is not defined. Multiply both sides of the equation by \left(n-6\right)\left(n-5\right), the least common multiple of 6-n,n-5.

$$\left(5-n\right)\left(4.085-3.353\right)=\left(n-6\right)\left(3.353-3.214\right)$$

Subtract 3.353 from 4.085 to get 0.732.

$$\left(5-n\right)\times 0.732=\left(n-6\right)\left(3.353-3.214\right)$$

Use the distributive property to multiply 5-n by 0.732.

$$3.66-0.732n=\left(n-6\right)\left(3.353-3.214\right)$$

Subtract 3.214 from 3.353 to get 0.139.

$$3.66-0.732n=\left(n-6\right)\times 0.139$$

Use the distributive property to multiply n-6 by 0.139.

$$3.66-0.732n=0.139n-0.834$$

Subtract 0.139n from both sides.

$$3.66-0.732n-0.139n=-0.834$$

Combine -0.732n and -0.139n to get -0.871n.

$$3.66-0.871n=-0.834$$

Subtract 3.66 from both sides.

$$-0.871n=-0.834-3.66$$

Subtract 3.66 from -0.834 to get -4.494.

$$-0.871n=-4.494$$

Divide both sides by -0.871.

$$n=\frac{-4.494}{-0.871}$$

Expand \frac{-4.494}{-0.871} by multiplying both numerator and the denominator by 1000.

$$n=\frac{-4494}{-871}$$

Fraction \frac{-4494}{-871} can be simplified to \frac{4494}{871} by removing the negative sign from both the numerator and the denominator.

$$n=\frac{4494}{871}$$