Solve Q_{1}=4-(1/2)(3.8-frac{Q_{1}}{2})

$$Q _ { 1 } = 4 - ( \frac { 1 } { 2 } ) ( 3.8 - \frac { Q _ { 1 } } { 2 } )$$

Solve for Q_1

$$Q_{1}=2.8$$

Steps for Solving Linear Equation

Add \frac{1}{2}\left(3.8-\frac{Q_{1}}{2}\right) to both sides.

$$Q_{1}+\frac{1}{2}\left(3.8-\frac{Q_{1}}{2}\right)=4$$

Use the distributive property to multiply \frac{1}{2} by 3.8-\frac{Q_{1}}{2}.

$$Q_{1}+\frac{1}{2}\times 3.8+\frac{1}{2}\left(-\frac{Q_{1}}{2}\right)=4$$

Convert decimal number 3.8 to fraction \frac{38}{10}. Reduce the fraction \frac{38}{10} to lowest terms by extracting and canceling out 2.

$$Q_{1}+\frac{1}{2}\times \frac{19}{5}+\frac{1}{2}\left(-\frac{Q_{1}}{2}\right)=4$$

Multiply \frac{1}{2} times \frac{19}{5} by multiplying numerator times numerator and denominator times denominator.

$$Q_{1}+\frac{1\times 19}{2\times 5}+\frac{1}{2}\left(-\frac{Q_{1}}{2}\right)=4$$

Do the multiplications in the fraction \frac{1\times 19}{2\times 5}.

$$Q_{1}+\frac{19}{10}+\frac{1}{2}\left(-\frac{Q_{1}}{2}\right)=4$$

Multiply \frac{1}{2} times -\frac{Q_{1}}{2} by multiplying numerator times numerator and denominator times denominator.

$$Q_{1}+\frac{19}{10}+\frac{-Q_{1}}{2\times 2}=4$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 10 and 2\times 2 is 20. Multiply \frac{19}{10} times \frac{2}{2}. Multiply \frac{-Q_{1}}{2\times 2} times \frac{5}{5}.

$$Q_{1}+\frac{19\times 2}{20}+\frac{5\left(-1\right)Q_{1}}{20}=4$$

Since \frac{19\times 2}{20} and \frac{5\left(-1\right)Q_{1}}{20} have the same denominator, add them by adding their numerators.

$$Q_{1}+\frac{19\times 2+5\left(-1\right)Q_{1}}{20}=4$$

Do the multiplications in 19\times 2+5\left(-1\right)Q_{1}.

$$Q_{1}+\frac{38-5Q_{1}}{20}=4$$

Divide each term of 38-5Q_{1} by 20 to get \frac{19}{10}-\frac{1}{4}Q_{1}.

$$Q_{1}+\frac{19}{10}-\frac{1}{4}Q_{1}=4$$

Combine Q_{1} and -\frac{1}{4}Q_{1} to get \frac{3}{4}Q_{1}.

$$\frac{3}{4}Q_{1}+\frac{19}{10}=4$$

Subtract \frac{19}{10} from both sides.

$$\frac{3}{4}Q_{1}=4-\frac{19}{10}$$

Convert 4 to fraction \frac{40}{10}.

$$\frac{3}{4}Q_{1}=\frac{40}{10}-\frac{19}{10}$$

Since \frac{40}{10} and \frac{19}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{4}Q_{1}=\frac{40-19}{10}$$

Subtract 19 from 40 to get 21.

$$\frac{3}{4}Q_{1}=\frac{21}{10}$$

Multiply both sides by \frac{4}{3}, the reciprocal of \frac{3}{4}.

$$Q_{1}=\frac{21}{10}\times \frac{4}{3}$$

Multiply \frac{21}{10} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$Q_{1}=\frac{21\times 4}{10\times 3}$$

Do the multiplications in the fraction \frac{21\times 4}{10\times 3}.

$$Q_{1}=\frac{84}{30}$$

Reduce the fraction \frac{84}{30} to lowest terms by extracting and canceling out 6.

$$Q_{1}=\frac{14}{5}$$