Solve 8/10*(15/8*7/8)+9/10=(frac{125}{1000}+frac{1}{2})x+frac{3}{9}

$$\frac { 8 } { 10 } \cdot ( \frac { 15 } { 8 } \times \frac { 7 } { 8 } ) + \frac { 9 } { 10 } = ( \frac { 125 } { 1000 } + \frac { 1 } { 2 } ) x + \frac { 3 } { 9 }$$

Solve for x

$$x = \frac{451}{150} = 3\frac{1}{150} \approx 3.006666667$$

Steps for Solving Linear Equation

Reduce the fraction \frac{8}{10} to lowest terms by extracting and canceling out 2.

$$\frac{4}{5}\times \frac{15}{8}\times \frac{7}{8}+\frac{9}{10}=\left(\frac{125}{1000}+\frac{1}{2}\right)x+\frac{3}{9}$$

Multiply \frac{4}{5} times \frac{15}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times 15}{5\times 8}\times \frac{7}{8}+\frac{9}{10}=\left(\frac{125}{1000}+\frac{1}{2}\right)x+\frac{3}{9}$$

Do the multiplications in the fraction \frac{4\times 15}{5\times 8}.

$$\frac{60}{40}\times \frac{7}{8}+\frac{9}{10}=\left(\frac{125}{1000}+\frac{1}{2}\right)x+\frac{3}{9}$$

Reduce the fraction \frac{60}{40} to lowest terms by extracting and canceling out 20.

$$\frac{3}{2}\times \frac{7}{8}+\frac{9}{10}=\left(\frac{125}{1000}+\frac{1}{2}\right)x+\frac{3}{9}$$

Multiply \frac{3}{2} times \frac{7}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 7}{2\times 8}+\frac{9}{10}=\left(\frac{125}{1000}+\frac{1}{2}\right)x+\frac{3}{9}$$

Do the multiplications in the fraction \frac{3\times 7}{2\times 8}.

$$\frac{21}{16}+\frac{9}{10}=\left(\frac{125}{1000}+\frac{1}{2}\right)x+\frac{3}{9}$$

Least common multiple of 16 and 10 is 80. Convert \frac{21}{16} and \frac{9}{10} to fractions with denominator 80.

$$\frac{105}{80}+\frac{72}{80}=\left(\frac{125}{1000}+\frac{1}{2}\right)x+\frac{3}{9}$$

Since \frac{105}{80} and \frac{72}{80} have the same denominator, add them by adding their numerators.

$$\frac{105+72}{80}=\left(\frac{125}{1000}+\frac{1}{2}\right)x+\frac{3}{9}$$

Add 105 and 72 to get 177.

$$\frac{177}{80}=\left(\frac{125}{1000}+\frac{1}{2}\right)x+\frac{3}{9}$$

Reduce the fraction \frac{125}{1000} to lowest terms by extracting and canceling out 125.

$$\frac{177}{80}=\left(\frac{1}{8}+\frac{1}{2}\right)x+\frac{3}{9}$$

Least common multiple of 8 and 2 is 8. Convert \frac{1}{8} and \frac{1}{2} to fractions with denominator 8.

$$\frac{177}{80}=\left(\frac{1}{8}+\frac{4}{8}\right)x+\frac{3}{9}$$

Since \frac{1}{8} and \frac{4}{8} have the same denominator, add them by adding their numerators.

$$\frac{177}{80}=\frac{1+4}{8}x+\frac{3}{9}$$

Add 1 and 4 to get 5.

$$\frac{177}{80}=\frac{5}{8}x+\frac{3}{9}$$

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

$$\frac{177}{80}=\frac{5}{8}x+\frac{1}{3}$$

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

$$\frac{5}{8}x+\frac{1}{3}=\frac{177}{80}$$

Subtract \frac{1}{3} from both sides.

$$\frac{5}{8}x=\frac{177}{80}-\frac{1}{3}$$

Least common multiple of 80 and 3 is 240. Convert \frac{177}{80} and \frac{1}{3} to fractions with denominator 240.

$$\frac{5}{8}x=\frac{531}{240}-\frac{80}{240}$$

Since \frac{531}{240} and \frac{80}{240} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{8}x=\frac{531-80}{240}$$

Subtract 80 from 531 to get 451.

$$\frac{5}{8}x=\frac{451}{240}$$

Multiply both sides by \frac{8}{5}, the reciprocal of \frac{5}{8}.

$$x=\frac{451}{240}\times \frac{8}{5}$$

Multiply \frac{451}{240} times \frac{8}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{451\times 8}{240\times 5}$$

Do the multiplications in the fraction \frac{451\times 8}{240\times 5}.

$$x=\frac{3608}{1200}$$

Reduce the fraction \frac{3608}{1200} to lowest terms by extracting and canceling out 8.

$$x=\frac{451}{150}$$