Solve 11.2%=beta(12%-4%)+4%

$$11.2 \% = \beta ( 12 \% - 4 \% ) + 4 \%$$

Solve for β

$$\beta =0.9$$

Steps for Solving Linear Equation

Expand \frac{11.2}{100} by multiplying both numerator and the denominator by 10.

$$\frac{112}{1000}=\beta \left(\frac{12}{100}-\frac{4}{100}\right)+\frac{4}{100}$$

Reduce the fraction \frac{112}{1000} to lowest terms by extracting and canceling out 8.

$$\frac{14}{125}=\beta \left(\frac{12}{100}-\frac{4}{100}\right)+\frac{4}{100}$$

Reduce the fraction \frac{12}{100} to lowest terms by extracting and canceling out 4.

$$\frac{14}{125}=\beta \left(\frac{3}{25}-\frac{4}{100}\right)+\frac{4}{100}$$

Reduce the fraction \frac{4}{100} to lowest terms by extracting and canceling out 4.

$$\frac{14}{125}=\beta \left(\frac{3}{25}-\frac{1}{25}\right)+\frac{4}{100}$$

Since \frac{3}{25} and \frac{1}{25} have the same denominator, subtract them by subtracting their numerators.

$$\frac{14}{125}=\beta \times \frac{3-1}{25}+\frac{4}{100}$$

Subtract 1 from 3 to get 2.

$$\frac{14}{125}=\beta \times \frac{2}{25}+\frac{4}{100}$$

Reduce the fraction \frac{4}{100} to lowest terms by extracting and canceling out 4.

$$\frac{14}{125}=\beta \times \frac{2}{25}+\frac{1}{25}$$

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

$$\beta \times \frac{2}{25}+\frac{1}{25}=\frac{14}{125}$$

Subtract \frac{1}{25} from both sides.

$$\beta \times \frac{2}{25}=\frac{14}{125}-\frac{1}{25}$$

Least common multiple of 125 and 25 is 125. Convert \frac{14}{125} and \frac{1}{25} to fractions with denominator 125.

$$\beta \times \frac{2}{25}=\frac{14}{125}-\frac{5}{125}$$

Since \frac{14}{125} and \frac{5}{125} have the same denominator, subtract them by subtracting their numerators.

$$\beta \times \frac{2}{25}=\frac{14-5}{125}$$

Subtract 5 from 14 to get 9.

$$\beta \times \frac{2}{25}=\frac{9}{125}$$

Multiply both sides by \frac{25}{2}, the reciprocal of \frac{2}{25}.

$$\beta =\frac{9}{125}\times \frac{25}{2}$$

Multiply \frac{9}{125} times \frac{25}{2} by multiplying numerator times numerator and denominator times denominator.

$$\beta =\frac{9\times 25}{125\times 2}$$

Do the multiplications in the fraction \frac{9\times 25}{125\times 2}.

$$\beta =\frac{225}{250}$$

Reduce the fraction \frac{225}{250} to lowest terms by extracting and canceling out 25.

$$\beta =\frac{9}{10}$$