Solve 3/4*0.008*200*0.4=(0.008*9/16*0.16+1/3*0.16)x

$$\frac { 3 } { 4 } \times 0.008 \times 200 \times 0.4 = ( 0.008 \times \frac { 9 } { 16 } \times 0.16 + \frac { 1 } { 3 } \times 0.16 ) x$$

Solve for x

$$x = \frac{18000}{2027} = 8\frac{1784}{2027} \approx 8.880118402$$

Steps for Solving Linear Equation

Convert decimal number 0.008 to fraction \frac{8}{1000}. Reduce the fraction \frac{8}{1000} to lowest terms by extracting and canceling out 8.

$$\frac{3}{4}\times \frac{1}{125}\times 200\times 0.4=\left(0.008\times \frac{9}{16}\times 0.16+\frac{1}{3}\times 0.16\right)x$$

Multiply \frac{3}{4} times \frac{1}{125} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 1}{4\times 125}\times 200\times 0.4=\left(0.008\times \frac{9}{16}\times 0.16+\frac{1}{3}\times 0.16\right)x$$

Do the multiplications in the fraction \frac{3\times 1}{4\times 125}.

$$\frac{3}{500}\times 200\times 0.4=\left(0.008\times \frac{9}{16}\times 0.16+\frac{1}{3}\times 0.16\right)x$$

Express \frac{3}{500}\times 200 as a single fraction.

$$\frac{3\times 200}{500}\times 0.4=\left(0.008\times \frac{9}{16}\times 0.16+\frac{1}{3}\times 0.16\right)x$$

Multiply 3 and 200 to get 600.

$$\frac{600}{500}\times 0.4=\left(0.008\times \frac{9}{16}\times 0.16+\frac{1}{3}\times 0.16\right)x$$

Reduce the fraction \frac{600}{500} to lowest terms by extracting and canceling out 100.

$$\frac{6}{5}\times 0.4=\left(0.008\times \frac{9}{16}\times 0.16+\frac{1}{3}\times 0.16\right)x$$

Convert decimal number 0.4 to fraction \frac{4}{10}. Reduce the fraction \frac{4}{10} to lowest terms by extracting and canceling out 2.

$$\frac{6}{5}\times \frac{2}{5}=\left(0.008\times \frac{9}{16}\times 0.16+\frac{1}{3}\times 0.16\right)x$$

Multiply \frac{6}{5} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{6\times 2}{5\times 5}=\left(0.008\times \frac{9}{16}\times 0.16+\frac{1}{3}\times 0.16\right)x$$

Do the multiplications in the fraction \frac{6\times 2}{5\times 5}.

$$\frac{12}{25}=\left(0.008\times \frac{9}{16}\times 0.16+\frac{1}{3}\times 0.16\right)x$$

Convert decimal number 0.008 to fraction \frac{8}{1000}. Reduce the fraction \frac{8}{1000} to lowest terms by extracting and canceling out 8.

$$\frac{12}{25}=\left(\frac{1}{125}\times \frac{9}{16}\times 0.16+\frac{1}{3}\times 0.16\right)x$$

Multiply \frac{1}{125} times \frac{9}{16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{12}{25}=\left(\frac{1\times 9}{125\times 16}\times 0.16+\frac{1}{3}\times 0.16\right)x$$

Do the multiplications in the fraction \frac{1\times 9}{125\times 16}.

$$\frac{12}{25}=\left(\frac{9}{2000}\times 0.16+\frac{1}{3}\times 0.16\right)x$$

Convert decimal number 0.16 to fraction \frac{16}{100}. Reduce the fraction \frac{16}{100} to lowest terms by extracting and canceling out 4.

$$\frac{12}{25}=\left(\frac{9}{2000}\times \frac{4}{25}+\frac{1}{3}\times 0.16\right)x$$

Multiply \frac{9}{2000} times \frac{4}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{12}{25}=\left(\frac{9\times 4}{2000\times 25}+\frac{1}{3}\times 0.16\right)x$$

Do the multiplications in the fraction \frac{9\times 4}{2000\times 25}.

$$\frac{12}{25}=\left(\frac{36}{50000}+\frac{1}{3}\times 0.16\right)x$$

Reduce the fraction \frac{36}{50000} to lowest terms by extracting and canceling out 4.

$$\frac{12}{25}=\left(\frac{9}{12500}+\frac{1}{3}\times 0.16\right)x$$

Convert decimal number 0.16 to fraction \frac{16}{100}. Reduce the fraction \frac{16}{100} to lowest terms by extracting and canceling out 4.

$$\frac{12}{25}=\left(\frac{9}{12500}+\frac{1}{3}\times \frac{4}{25}\right)x$$

Multiply \frac{1}{3} times \frac{4}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{12}{25}=\left(\frac{9}{12500}+\frac{1\times 4}{3\times 25}\right)x$$

Do the multiplications in the fraction \frac{1\times 4}{3\times 25}.

$$\frac{12}{25}=\left(\frac{9}{12500}+\frac{4}{75}\right)x$$

Least common multiple of 12500 and 75 is 37500. Convert \frac{9}{12500} and \frac{4}{75} to fractions with denominator 37500.

$$\frac{12}{25}=\left(\frac{27}{37500}+\frac{2000}{37500}\right)x$$

Since \frac{27}{37500} and \frac{2000}{37500} have the same denominator, add them by adding their numerators.

$$\frac{12}{25}=\frac{27+2000}{37500}x$$

Add 27 and 2000 to get 2027.

$$\frac{12}{25}=\frac{2027}{37500}x$$

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

$$\frac{2027}{37500}x=\frac{12}{25}$$

Multiply both sides by \frac{37500}{2027}, the reciprocal of \frac{2027}{37500}.

$$x=\frac{12}{25}\times \frac{37500}{2027}$$

Multiply \frac{12}{25} times \frac{37500}{2027} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{12\times 37500}{25\times 2027}$$

Do the multiplications in the fraction \frac{12\times 37500}{25\times 2027}.

$$x=\frac{450000}{50675}$$

Reduce the fraction \frac{450000}{50675} to lowest terms by extracting and canceling out 25.

$$x=\frac{18000}{2027}$$