Solve 8/6=2y+4/7.5

$$\frac{ 8 }{ 6 } = \frac{ 2y+4 }{ 7.5 }$$

Solve for y

$$y=3$$

Steps for Solving Linear Equation

Reduce the fraction \frac{8}{6} to lowest terms by extracting and canceling out 2.

$$\frac{4}{3}=\frac{2y+4}{7.5}$$

Divide each term of 2y+4 by 7.5 to get \frac{2y}{7.5}+\frac{4}{7.5}.

$$\frac{4}{3}=\frac{2y}{7.5}+\frac{4}{7.5}$$

Divide 2y by 7.5 to get \frac{4}{15}y.

$$\frac{4}{3}=\frac{4}{15}y+\frac{4}{7.5}$$

Expand \frac{4}{7.5} by multiplying both numerator and the denominator by 10.

$$\frac{4}{3}=\frac{4}{15}y+\frac{40}{75}$$

Reduce the fraction \frac{40}{75} to lowest terms by extracting and canceling out 5.

$$\frac{4}{3}=\frac{4}{15}y+\frac{8}{15}$$

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

$$\frac{4}{15}y+\frac{8}{15}=\frac{4}{3}$$

Subtract \frac{8}{15} from both sides.

$$\frac{4}{15}y=\frac{4}{3}-\frac{8}{15}$$

Least common multiple of 3 and 15 is 15. Convert \frac{4}{3} and \frac{8}{15} to fractions with denominator 15.

$$\frac{4}{15}y=\frac{20}{15}-\frac{8}{15}$$

Since \frac{20}{15} and \frac{8}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4}{15}y=\frac{20-8}{15}$$

Subtract 8 from 20 to get 12.

$$\frac{4}{15}y=\frac{12}{15}$$

Reduce the fraction \frac{12}{15} to lowest terms by extracting and canceling out 3.

$$\frac{4}{15}y=\frac{4}{5}$$

Divide both sides by \frac{4}{15}.

$$y=\frac{\frac{4}{5}}{\frac{4}{15}}$$

Express \frac{\frac{4}{5}}{\frac{4}{15}} as a single fraction.

$$y=\frac{4}{5\times \frac{4}{15}}$$

Multiply 5 and \frac{4}{15} to get \frac{4}{3}.

$$y=\frac{4}{\frac{4}{3}}$$