Solve 90/57-x=4left(92/4+13/4right)

$$\frac{ 90 }{ 57-x } = 4 \left( 9 \frac{ 2 }{ 4 } +1 \frac{ 3 }{ 4 } \right)$$

Solve for x

$$x=55$$

Steps for Solving Linear Equation

Variable x cannot be equal to 57 since division by zero is not defined. Multiply both sides of the equation by 4\left(x-57\right), the least common multiple of 57-x,4.

$$-4\times 90=4\left(\frac{9\times 4+2}{4}+\frac{1\times 4+3}{4}\right)\times 4\left(x-57\right)$$

Multiply -4 and 90 to get -360.

$$-360=4\left(\frac{9\times 4+2}{4}+\frac{1\times 4+3}{4}\right)\times 4\left(x-57\right)$$

Multiply 9 and 4 to get 36.

$$-360=4\left(\frac{36+2}{4}+\frac{1\times 4+3}{4}\right)\times 4\left(x-57\right)$$

Add 36 and 2 to get 38.

$$-360=4\left(\frac{38}{4}+\frac{1\times 4+3}{4}\right)\times 4\left(x-57\right)$$

Reduce the fraction \frac{38}{4} to lowest terms by extracting and canceling out 2.

$$-360=4\left(\frac{19}{2}+\frac{1\times 4+3}{4}\right)\times 4\left(x-57\right)$$

Multiply 1 and 4 to get 4.

$$-360=4\left(\frac{19}{2}+\frac{4+3}{4}\right)\times 4\left(x-57\right)$$

Add 4 and 3 to get 7.

$$-360=4\left(\frac{19}{2}+\frac{7}{4}\right)\times 4\left(x-57\right)$$

Add \frac{19}{2} and \frac{7}{4} to get \frac{45}{4}.

$$-360=4\times \frac{45}{4}\times 4\left(x-57\right)$$

Multiply 4 and \frac{45}{4} to get 45.

$$-360=45\times 4\left(x-57\right)$$

Multiply 45 and 4 to get 180.

$$-360=180\left(x-57\right)$$

Use the distributive property to multiply 180 by x-57.

$$-360=180x-10260$$

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

$$180x-10260=-360$$

Add 10260 to both sides.

$$180x=-360+10260$$

Add -360 and 10260 to get 9900.

$$180x=9900$$

Divide both sides by 180.

$$x=\frac{9900}{180}$$

Divide 9900 by 180 to get 55.

$$x=55$$