Solve (34.6/4.6)-(2.3*4.9)=(32-a)+(-21.1+10.6)

$$( 34.6 / 4.6 ) - ( 2.3 \times 4.9 ) = ( 32 - a ) + ( - 21.1 + 10.6 )$$

Solve for a

$$a=27.58$$

Steps for Solving Linear Equation

Expand \frac{34.6}{4} by multiplying both numerator and the denominator by 10.

$$\frac{346}{40}\times 0.6-2.3\times 4.9=32-a-21.1+10.6$$

Reduce the fraction \frac{346}{40} to lowest terms by extracting and canceling out 2.

$$\frac{173}{20}\times 0.6-2.3\times 4.9=32-a-21.1+10.6$$

Convert decimal number 0.6 to fraction \frac{6}{10}. Reduce the fraction \frac{6}{10} to lowest terms by extracting and canceling out 2.

$$\frac{173}{20}\times \frac{3}{5}-2.3\times 4.9=32-a-21.1+10.6$$

Multiply \frac{173}{20} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{173\times 3}{20\times 5}-2.3\times 4.9=32-a-21.1+10.6$$

Do the multiplications in the fraction \frac{173\times 3}{20\times 5}.

$$\frac{519}{100}-2.3\times 4.9=32-a-21.1+10.6$$

Multiply 2.3 and 4.9 to get 11.27.

$$\frac{519}{100}-11.27=32-a-21.1+10.6$$

Convert decimal number 11.27 to fraction \frac{1127}{100}.

$$\frac{519}{100}-\frac{1127}{100}=32-a-21.1+10.6$$

Since \frac{519}{100} and \frac{1127}{100} have the same denominator, subtract them by subtracting their numerators.

$$\frac{519-1127}{100}=32-a-21.1+10.6$$

Subtract 1127 from 519 to get -608.

$$\frac{-608}{100}=32-a-21.1+10.6$$

Reduce the fraction \frac{-608}{100} to lowest terms by extracting and canceling out 4.

$$-\frac{152}{25}=32-a-21.1+10.6$$

Subtract 21.1 from 32 to get 10.9.

$$-\frac{152}{25}=10.9-a+10.6$$

Add 10.9 and 10.6 to get 21.5.

$$-\frac{152}{25}=21.5-a$$

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

$$21.5-a=-\frac{152}{25}$$

Subtract 21.5 from both sides.

$$-a=-\frac{152}{25}-21.5$$

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.

$$-a=-\frac{152}{25}-\frac{43}{2}$$

Least common multiple of 25 and 2 is 50. Convert -\frac{152}{25} and \frac{43}{2} to fractions with denominator 50.

$$-a=-\frac{304}{50}-\frac{1075}{50}$$

Since -\frac{304}{50} and \frac{1075}{50} have the same denominator, subtract them by subtracting their numerators.

$$-a=\frac{-304-1075}{50}$$

Subtract 1075 from -304 to get -1379.

$$-a=-\frac{1379}{50}$$

Multiply both sides by -1.

$$a=\frac{1379}{50}$$