Solve 0.4y+0.9/0.5-0.3+0.2y/0.3=1

$$\frac { 0.4 y + 0.9 } { 0.5 } - \frac { 0.3 + 0.2 y } { 0.3 } = 1$$

Solve for y

$$y=1.5$$

Steps for Solving Linear Equation

Divide each term of 0.4y+0.9 by 0.5 to get \frac{0.4y}{0.5}+\frac{0.9}{0.5}.

$$\frac{0.4y}{0.5}+\frac{0.9}{0.5}-\frac{0.3+0.2y}{0.3}=1$$

Divide 0.4y by 0.5 to get 0.8y.

$$0.8y+\frac{0.9}{0.5}-\frac{0.3+0.2y}{0.3}=1$$

Expand \frac{0.9}{0.5} by multiplying both numerator and the denominator by 10.

$$0.8y+\frac{9}{5}-\frac{0.3+0.2y}{0.3}=1$$

Divide each term of 0.3+0.2y by 0.3 to get \frac{0.3}{0.3}+\frac{0.2y}{0.3}.

$$0.8y+\frac{9}{5}-\left(\frac{0.3}{0.3}+\frac{0.2y}{0.3}\right)=1$$

Divide 0.3 by 0.3 to get 1.

$$0.8y+\frac{9}{5}-\left(1+\frac{0.2y}{0.3}\right)=1$$

Divide 0.2y by 0.3 to get \frac{2}{3}y.

$$0.8y+\frac{9}{5}-\left(1+\frac{2}{3}y\right)=1$$

To find the opposite of 1+\frac{2}{3}y, find the opposite of each term.

$$0.8y+\frac{9}{5}-1-\frac{2}{3}y=1$$

Convert 1 to fraction \frac{5}{5}.

$$0.8y+\frac{9}{5}-\frac{5}{5}-\frac{2}{3}y=1$$

Since \frac{9}{5} and \frac{5}{5} have the same denominator, subtract them by subtracting their numerators.

$$0.8y+\frac{9-5}{5}-\frac{2}{3}y=1$$

Subtract 5 from 9 to get 4.

$$0.8y+\frac{4}{5}-\frac{2}{3}y=1$$

Combine 0.8y and -\frac{2}{3}y to get \frac{2}{15}y.

$$\frac{2}{15}y+\frac{4}{5}=1$$

Subtract \frac{4}{5} from both sides.

$$\frac{2}{15}y=1-\frac{4}{5}$$

Convert 1 to fraction \frac{5}{5}.

$$\frac{2}{15}y=\frac{5}{5}-\frac{4}{5}$$

Since \frac{5}{5} and \frac{4}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{15}y=\frac{5-4}{5}$$

Subtract 4 from 5 to get 1.

$$\frac{2}{15}y=\frac{1}{5}$$

Divide both sides by \frac{2}{15}.

$$y=\frac{\frac{1}{5}}{\frac{2}{15}}$$

Express \frac{\frac{1}{5}}{\frac{2}{15}} as a single fraction.

$$y=\frac{1}{5\times \frac{2}{15}}$$

Multiply 5 and \frac{2}{15} to get \frac{2}{3}.

$$y=\frac{1}{\frac{2}{3}}$$