Solve (7,2-3,2x):5/2+18,5=4/5

$$( 7,2 - 3,2 x ) : \frac { 5 } { 2 } + 18,5 = \frac { 4 } { 5 }$$

Solve for x

$$x=16,078125$$

Steps for Solving Linear Equation

Divide each term of 7,2-3,2x by \frac{5}{2} to get \frac{7,2}{\frac{5}{2}}+\frac{-3,2x}{\frac{5}{2}}.

$$\frac{7,2}{\frac{5}{2}}+\frac{-3,2x}{\frac{5}{2}}+18,5=\frac{4}{5}$$

Divide 7,2 by \frac{5}{2} by multiplying 7,2 by the reciprocal of \frac{5}{2}.

$$7,2\times \frac{2}{5}+\frac{-3,2x}{\frac{5}{2}}+18,5=\frac{4}{5}$$

Convert decimal number 7,2 to fraction \frac{72}{10}. Reduce the fraction \frac{72}{10} to lowest terms by extracting and canceling out 2.

$$\frac{36}{5}\times \frac{2}{5}+\frac{-3,2x}{\frac{5}{2}}+18,5=\frac{4}{5}$$

Multiply \frac{36}{5} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{36\times 2}{5\times 5}+\frac{-3,2x}{\frac{5}{2}}+18,5=\frac{4}{5}$$

Do the multiplications in the fraction \frac{36\times 2}{5\times 5}.

$$\frac{72}{25}+\frac{-3,2x}{\frac{5}{2}}+18,5=\frac{4}{5}$$

Divide -3,2x by \frac{5}{2} to get -\frac{32}{25}x.

$$\frac{72}{25}-\frac{32}{25}x+18,5=\frac{4}{5}$$

Convert decimal number 18,5 to fraction \frac{185}{10}. Reduce the fraction \frac{185}{10} to lowest terms by extracting and canceling out 5.

$$\frac{72}{25}-\frac{32}{25}x+\frac{37}{2}=\frac{4}{5}$$

Least common multiple of 25 and 2 is 50. Convert \frac{72}{25} and \frac{37}{2} to fractions with denominator 50.

$$\frac{144}{50}-\frac{32}{25}x+\frac{925}{50}=\frac{4}{5}$$

Since \frac{144}{50} and \frac{925}{50} have the same denominator, add them by adding their numerators.

$$\frac{144+925}{50}-\frac{32}{25}x=\frac{4}{5}$$

Add 144 and 925 to get 1069.

$$\frac{1069}{50}-\frac{32}{25}x=\frac{4}{5}$$

Subtract \frac{1069}{50} from both sides.

$$-\frac{32}{25}x=\frac{4}{5}-\frac{1069}{50}$$

Least common multiple of 5 and 50 is 50. Convert \frac{4}{5} and \frac{1069}{50} to fractions with denominator 50.

$$-\frac{32}{25}x=\frac{40}{50}-\frac{1069}{50}$$

Since \frac{40}{50} and \frac{1069}{50} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{32}{25}x=\frac{40-1069}{50}$$

Subtract 1069 from 40 to get -1029.

$$-\frac{32}{25}x=-\frac{1029}{50}$$

Multiply both sides by -\frac{25}{32}, the reciprocal of -\frac{32}{25}.

$$x=-\frac{1029}{50}\left(-\frac{25}{32}\right)$$

Multiply -\frac{1029}{50} times -\frac{25}{32} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-1029\left(-25\right)}{50\times 32}$$

Do the multiplications in the fraction \frac{-1029\left(-25\right)}{50\times 32}.

$$x=\frac{25725}{1600}$$

Reduce the fraction \frac{25725}{1600} to lowest terms by extracting and canceling out 25.

$$x=\frac{1029}{64}$$