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

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

Solve for x

$$x = \frac{113}{2} = 56\frac{1}{2} = 56.5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4.

$$360\left(57-x\right)=16\left(\frac{9\times 4+2}{4}+\frac{1\times 4+3}{4}\right)$$

Use the distributive property to multiply 360 by 57-x.

$$20520-360x=16\left(\frac{9\times 4+2}{4}+\frac{1\times 4+3}{4}\right)$$

Multiply 9 and 4 to get 36.

$$20520-360x=16\left(\frac{36+2}{4}+\frac{1\times 4+3}{4}\right)$$

Add 36 and 2 to get 38.

$$20520-360x=16\left(\frac{38}{4}+\frac{1\times 4+3}{4}\right)$$

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

$$20520-360x=16\left(\frac{19}{2}+\frac{1\times 4+3}{4}\right)$$

Multiply 1 and 4 to get 4.

$$20520-360x=16\left(\frac{19}{2}+\frac{4+3}{4}\right)$$

Add 4 and 3 to get 7.

$$20520-360x=16\left(\frac{19}{2}+\frac{7}{4}\right)$$

Least common multiple of 2 and 4 is 4. Convert \frac{19}{2} and \frac{7}{4} to fractions with denominator 4.

$$20520-360x=16\left(\frac{38}{4}+\frac{7}{4}\right)$$

Since \frac{38}{4} and \frac{7}{4} have the same denominator, add them by adding their numerators.

$$20520-360x=16\times \frac{38+7}{4}$$

Add 38 and 7 to get 45.

$$20520-360x=16\times \frac{45}{4}$$

Express 16\times \frac{45}{4} as a single fraction.

$$20520-360x=\frac{16\times 45}{4}$$

Multiply 16 and 45 to get 720.

$$20520-360x=\frac{720}{4}$$

Divide 720 by 4 to get 180.

$$20520-360x=180$$

Subtract 20520 from both sides.

$$-360x=180-20520$$

Subtract 20520 from 180 to get -20340.

$$-360x=-20340$$

Divide both sides by -360.

$$x=\frac{-20340}{-360}$$

Reduce the fraction \frac{-20340}{-360} to lowest terms by extracting and canceling out -180.

$$x=\frac{113}{2}$$