Solve 818+82beta/1511+1518=1064beta/5558+8

$$\frac { 818 + 82 \beta } { 1511 + 1518 } = \frac { 1064 \beta } { 5558 + 8 }$$

Solve for β

$$\beta =\frac{1138247}{691611}\approx 1.64579077$$

Steps for Solving Linear Equation

Add 1511 and 1518 to get 3029.

$$\frac{818+82\beta }{3029}=\frac{1064\beta }{5558+8}$$

Add 5558 and 8 to get 5566.

$$\frac{818+82\beta }{3029}=\frac{1064\beta }{5566}$$

Divide 1064\beta by 5566 to get \frac{532}{2783}\beta .

$$\frac{818+82\beta }{3029}=\frac{532}{2783}\beta$$

Divide each term of 818+82\beta by 3029 to get \frac{818}{3029}+\frac{82}{3029}\beta .

$$\frac{818}{3029}+\frac{82}{3029}\beta =\frac{532}{2783}\beta$$

Subtract \frac{532}{2783}\beta from both sides.

$$\frac{818}{3029}+\frac{82}{3029}\beta -\frac{532}{2783}\beta =0$$

Combine \frac{82}{3029}\beta and -\frac{532}{2783}\beta to get -\frac{1383222}{8429707}\beta .

$$\frac{818}{3029}-\frac{1383222}{8429707}\beta =0$$

Subtract \frac{818}{3029} from both sides. Anything subtracted from zero gives its negation.

$$-\frac{1383222}{8429707}\beta =-\frac{818}{3029}$$

Multiply both sides by -\frac{8429707}{1383222}, the reciprocal of -\frac{1383222}{8429707}.

$$\beta =-\frac{818}{3029}\left(-\frac{8429707}{1383222}\right)$$

Multiply -\frac{818}{3029} times -\frac{8429707}{1383222} by multiplying numerator times numerator and denominator times denominator.

$$\beta =\frac{-818\left(-8429707\right)}{3029\times 1383222}$$

Do the multiplications in the fraction \frac{-818\left(-8429707\right)}{3029\times 1383222}.

$$\beta =\frac{6895500326}{4189779438}$$

Reduce the fraction \frac{6895500326}{4189779438} to lowest terms by extracting and canceling out 6058.

$$\beta =\frac{1138247}{691611}$$