Solve 57/2=22/7r+90/7

$$\frac { 57 } { 2 } = \frac { 22 } { 7 } r + \frac { 90 } { 7 }$$

Solve for r

$$r = \frac{219}{44} = 4\frac{43}{44} \approx 4.977272727$$

Steps for Solving Linear Equation

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

$$\frac{22}{7}r+\frac{90}{7}=\frac{57}{2}$$

Subtract \frac{90}{7} from both sides.

$$\frac{22}{7}r=\frac{57}{2}-\frac{90}{7}$$

Least common multiple of 2 and 7 is 14. Convert \frac{57}{2} and \frac{90}{7} to fractions with denominator 14.

$$\frac{22}{7}r=\frac{399}{14}-\frac{180}{14}$$

Since \frac{399}{14} and \frac{180}{14} have the same denominator, subtract them by subtracting their numerators.

$$\frac{22}{7}r=\frac{399-180}{14}$$

Subtract 180 from 399 to get 219.

$$\frac{22}{7}r=\frac{219}{14}$$

Multiply both sides by \frac{7}{22}, the reciprocal of \frac{22}{7}.

$$r=\frac{219}{14}\times \frac{7}{22}$$

Multiply \frac{219}{14} times \frac{7}{22} by multiplying numerator times numerator and denominator times denominator.

$$r=\frac{219\times 7}{14\times 22}$$

Do the multiplications in the fraction \frac{219\times 7}{14\times 22}.

$$r=\frac{1533}{308}$$

Reduce the fraction \frac{1533}{308} to lowest terms by extracting and canceling out 7.

$$r=\frac{219}{44}$$