Solve 0.4x+0.9/0.5-0.1x-0.5/0.2=0.03+0.02x/0.03

$$\frac { 0.4 x + 0.9 } { 0.5 } - \frac { 0.1 x - 0.5 } { 0.2 } = \frac { 0.03 + 0.02 x } { 0.03 }$$

Solve for x

$$x=9$$

Steps for Solving Linear Equation

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

$$\frac{0.4x}{0.5}+\frac{0.9}{0.5}-\frac{0.1x-0.5}{0.2}=\frac{0.03+0.02x}{0.03}$$

Divide 0.4x by 0.5 to get 0.8x.

$$0.8x+\frac{0.9}{0.5}-\frac{0.1x-0.5}{0.2}=\frac{0.03+0.02x}{0.03}$$

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

$$0.8x+\frac{9}{5}-\frac{0.1x-0.5}{0.2}=\frac{0.03+0.02x}{0.03}$$

Divide each term of 0.1x-0.5 by 0.2 to get \frac{0.1x}{0.2}+\frac{-0.5}{0.2}.

$$0.8x+\frac{9}{5}-\left(\frac{0.1x}{0.2}+\frac{-0.5}{0.2}\right)=\frac{0.03+0.02x}{0.03}$$

Divide 0.1x by 0.2 to get 0.5x.

$$0.8x+\frac{9}{5}-\left(0.5x+\frac{-0.5}{0.2}\right)=\frac{0.03+0.02x}{0.03}$$

Expand \frac{-0.5}{0.2} by multiplying both numerator and the denominator by 10.

$$0.8x+\frac{9}{5}-\left(0.5x+\frac{-5}{2}\right)=\frac{0.03+0.02x}{0.03}$$

Fraction \frac{-5}{2} can be rewritten as -\frac{5}{2} by extracting the negative sign.

$$0.8x+\frac{9}{5}-\left(0.5x-\frac{5}{2}\right)=\frac{0.03+0.02x}{0.03}$$

To find the opposite of 0.5x-\frac{5}{2}, find the opposite of each term.

$$0.8x+\frac{9}{5}-0.5x-\left(-\frac{5}{2}\right)=\frac{0.03+0.02x}{0.03}$$

The opposite of -\frac{5}{2} is \frac{5}{2}.

$$0.8x+\frac{9}{5}-0.5x+\frac{5}{2}=\frac{0.03+0.02x}{0.03}$$

Combine 0.8x and -0.5x to get 0.3x.

$$0.3x+\frac{9}{5}+\frac{5}{2}=\frac{0.03+0.02x}{0.03}$$

Least common multiple of 5 and 2 is 10. Convert \frac{9}{5} and \frac{5}{2} to fractions with denominator 10.

$$0.3x+\frac{18}{10}+\frac{25}{10}=\frac{0.03+0.02x}{0.03}$$

Since \frac{18}{10} and \frac{25}{10} have the same denominator, add them by adding their numerators.

$$0.3x+\frac{18+25}{10}=\frac{0.03+0.02x}{0.03}$$

Add 18 and 25 to get 43.

$$0.3x+\frac{43}{10}=\frac{0.03+0.02x}{0.03}$$

Divide each term of 0.03+0.02x by 0.03 to get \frac{0.03}{0.03}+\frac{0.02x}{0.03}.

$$0.3x+\frac{43}{10}=\frac{0.03}{0.03}+\frac{0.02x}{0.03}$$

Divide 0.03 by 0.03 to get 1.

$$0.3x+\frac{43}{10}=1+\frac{0.02x}{0.03}$$

Divide 0.02x by 0.03 to get \frac{2}{3}x.

$$0.3x+\frac{43}{10}=1+\frac{2}{3}x$$

Subtract \frac{2}{3}x from both sides.

$$0.3x+\frac{43}{10}-\frac{2}{3}x=1$$

Combine 0.3x and -\frac{2}{3}x to get -\frac{11}{30}x.

$$-\frac{11}{30}x+\frac{43}{10}=1$$

Subtract \frac{43}{10} from both sides.

$$-\frac{11}{30}x=1-\frac{43}{10}$$

Convert 1 to fraction \frac{10}{10}.

$$-\frac{11}{30}x=\frac{10}{10}-\frac{43}{10}$$

Since \frac{10}{10} and \frac{43}{10} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{11}{30}x=\frac{10-43}{10}$$

Subtract 43 from 10 to get -33.

$$-\frac{11}{30}x=-\frac{33}{10}$$

Divide both sides by -\frac{11}{30}.

$$x=\frac{-\frac{33}{10}}{-\frac{11}{30}}$$

Express \frac{-\frac{33}{10}}{-\frac{11}{30}} as a single fraction.

$$x=\frac{-33}{10\left(-\frac{11}{30}\right)}$$

Multiply 10 and -\frac{11}{30} to get -\frac{11}{3}.

$$x=\frac{-33}{-\frac{11}{3}}$$