Solve 4.3*(5-x)-1/7*(2.1x-0.77)=0.09-2x

$$4.3 \times (5-x)- \frac{ 1 }{ 7 } \times (2.1x-0.77)=0.09-2x$$

Solve for x

$$x = \frac{538}{65} = 8\frac{18}{65} \approx 8.276923077$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4.3 by 5-x.

$$21.5-4.3x-\frac{1}{7}\left(2.1x-0.77\right)=0.09-2x$$

Use the distributive property to multiply -\frac{1}{7} by 2.1x-0.77.

$$21.5-4.3x-\frac{1}{7}\times 2.1x-\frac{1}{7}\left(-0.77\right)=0.09-2x$$

Convert decimal number 2.1 to fraction \frac{21}{10}.

$$21.5-4.3x-\frac{1}{7}\times \frac{21}{10}x-\frac{1}{7}\left(-0.77\right)=0.09-2x$$

Multiply -\frac{1}{7} times \frac{21}{10} by multiplying numerator times numerator and denominator times denominator.

$$21.5-4.3x+\frac{-21}{7\times 10}x-\frac{1}{7}\left(-0.77\right)=0.09-2x$$

Do the multiplications in the fraction \frac{-21}{7\times 10}.

$$21.5-4.3x+\frac{-21}{70}x-\frac{1}{7}\left(-0.77\right)=0.09-2x$$

Reduce the fraction \frac{-21}{70} to lowest terms by extracting and canceling out 7.

$$21.5-4.3x-\frac{3}{10}x-\frac{1}{7}\left(-0.77\right)=0.09-2x$$

Convert decimal number -0.77 to fraction -\frac{77}{100}.

$$21.5-4.3x-\frac{3}{10}x-\frac{1}{7}\left(-\frac{77}{100}\right)=0.09-2x$$

Multiply -\frac{1}{7} times -\frac{77}{100} by multiplying numerator times numerator and denominator times denominator.

$$21.5-4.3x-\frac{3}{10}x+\frac{-\left(-77\right)}{7\times 100}=0.09-2x$$

Do the multiplications in the fraction \frac{-\left(-77\right)}{7\times 100}.

$$21.5-4.3x-\frac{3}{10}x+\frac{77}{700}=0.09-2x$$

Reduce the fraction \frac{77}{700} to lowest terms by extracting and canceling out 7.

$$21.5-4.3x-\frac{3}{10}x+\frac{11}{100}=0.09-2x$$

Combine -4.3x and -\frac{3}{10}x to get -\frac{23}{5}x.

$$21.5-\frac{23}{5}x+\frac{11}{100}=0.09-2x$$

Convert decimal number 21.5 to fraction \frac{215}{10}. Reduce the fraction \frac{215}{10} to lowest terms by extracting and canceling out 5.

$$\frac{43}{2}-\frac{23}{5}x+\frac{11}{100}=0.09-2x$$

Least common multiple of 2 and 100 is 100. Convert \frac{43}{2} and \frac{11}{100} to fractions with denominator 100.

$$\frac{2150}{100}-\frac{23}{5}x+\frac{11}{100}=0.09-2x$$

Since \frac{2150}{100} and \frac{11}{100} have the same denominator, add them by adding their numerators.

$$\frac{2150+11}{100}-\frac{23}{5}x=0.09-2x$$

Add 2150 and 11 to get 2161.

$$\frac{2161}{100}-\frac{23}{5}x=0.09-2x$$

Add 2x to both sides.

$$\frac{2161}{100}-\frac{23}{5}x+2x=0.09$$

Combine -\frac{23}{5}x and 2x to get -\frac{13}{5}x.

$$\frac{2161}{100}-\frac{13}{5}x=0.09$$

Subtract \frac{2161}{100} from both sides.

$$-\frac{13}{5}x=0.09-\frac{2161}{100}$$

Convert decimal number 0.09 to fraction \frac{9}{100}.

$$-\frac{13}{5}x=\frac{9}{100}-\frac{2161}{100}$$

Since \frac{9}{100} and \frac{2161}{100} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{13}{5}x=\frac{9-2161}{100}$$

Subtract 2161 from 9 to get -2152.

$$-\frac{13}{5}x=\frac{-2152}{100}$$

Reduce the fraction \frac{-2152}{100} to lowest terms by extracting and canceling out 4.

$$-\frac{13}{5}x=-\frac{538}{25}$$

Multiply both sides by -\frac{5}{13}, the reciprocal of -\frac{13}{5}.

$$x=-\frac{538}{25}\left(-\frac{5}{13}\right)$$

Multiply -\frac{538}{25} times -\frac{5}{13} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-538\left(-5\right)}{25\times 13}$$

Do the multiplications in the fraction \frac{-538\left(-5\right)}{25\times 13}.

$$x=\frac{2690}{325}$$

Reduce the fraction \frac{2690}{325} to lowest terms by extracting and canceling out 5.

$$x=\frac{538}{65}$$