Solve 4/40+y+16/40=31/40+6/40

$$\frac { 4 } { 40 } + y + \frac { 16 } { 40 } = \frac { 31 } { 40 } + \frac { 6 } { 40 }$$

Solve for y

$$y=\frac{17}{40}=0.425$$

Steps for Solving Linear Equation

Reduce the fraction \frac{4}{40} to lowest terms by extracting and canceling out 4.

$$\frac{1}{10}+y+\frac{16}{40}=\frac{31}{40}+\frac{6}{40}$$

Reduce the fraction \frac{16}{40} to lowest terms by extracting and canceling out 8.

$$\frac{1}{10}+y+\frac{2}{5}=\frac{31}{40}+\frac{6}{40}$$

Least common multiple of 10 and 5 is 10. Convert \frac{1}{10} and \frac{2}{5} to fractions with denominator 10.

$$\frac{1}{10}+y+\frac{4}{10}=\frac{31}{40}+\frac{6}{40}$$

Since \frac{1}{10} and \frac{4}{10} have the same denominator, add them by adding their numerators.

$$\frac{1+4}{10}+y=\frac{31}{40}+\frac{6}{40}$$

Add 1 and 4 to get 5.

$$\frac{5}{10}+y=\frac{31}{40}+\frac{6}{40}$$

Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{1}{2}+y=\frac{31}{40}+\frac{6}{40}$$

Reduce the fraction \frac{6}{40} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}+y=\frac{31}{40}+\frac{3}{20}$$

Least common multiple of 40 and 20 is 40. Convert \frac{31}{40} and \frac{3}{20} to fractions with denominator 40.

$$\frac{1}{2}+y=\frac{31}{40}+\frac{6}{40}$$

Since \frac{31}{40} and \frac{6}{40} have the same denominator, add them by adding their numerators.

$$\frac{1}{2}+y=\frac{31+6}{40}$$

Add 31 and 6 to get 37.

$$\frac{1}{2}+y=\frac{37}{40}$$

Subtract \frac{1}{2} from both sides.

$$y=\frac{37}{40}-\frac{1}{2}$$

Least common multiple of 40 and 2 is 40. Convert \frac{37}{40} and \frac{1}{2} to fractions with denominator 40.

$$y=\frac{37}{40}-\frac{20}{40}$$

Since \frac{37}{40} and \frac{20}{40} have the same denominator, subtract them by subtracting their numerators.

$$y=\frac{37-20}{40}$$

Subtract 20 from 37 to get 17.

$$y=\frac{17}{40}$$