Solve 0.1x-0.2/0.5-0.01x+0.03/0.1=1

$$\frac { 0.1 x - 0.2 } { 0.5 } - \frac { 0.01 x + 0.03 } { 0.1 } = 1$$

Solve for x

$$x=17$$

Steps for Solving Linear Equation

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

$$\frac{0.1x}{0.5}+\frac{-0.2}{0.5}-\frac{0.01x+0.03}{0.1}=1$$

Divide 0.1x by 0.5 to get 0.2x.

$$0.2x+\frac{-0.2}{0.5}-\frac{0.01x+0.03}{0.1}=1$$

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

$$0.2x+\frac{-2}{5}-\frac{0.01x+0.03}{0.1}=1$$

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

$$0.2x-\frac{2}{5}-\frac{0.01x+0.03}{0.1}=1$$

Divide each term of 0.01x+0.03 by 0.1 to get \frac{0.01x}{0.1}+\frac{0.03}{0.1}.

$$0.2x-\frac{2}{5}-\left(\frac{0.01x}{0.1}+\frac{0.03}{0.1}\right)=1$$

Divide 0.01x by 0.1 to get 0.1x.

$$0.2x-\frac{2}{5}-\left(0.1x+\frac{0.03}{0.1}\right)=1$$

Expand \frac{0.03}{0.1} by multiplying both numerator and the denominator by 100.

$$0.2x-\frac{2}{5}-\left(0.1x+\frac{3}{10}\right)=1$$

To find the opposite of 0.1x+\frac{3}{10}, find the opposite of each term.

$$0.2x-\frac{2}{5}-0.1x-\frac{3}{10}=1$$

Combine 0.2x and -0.1x to get 0.1x.

$$0.1x-\frac{2}{5}-\frac{3}{10}=1$$

Least common multiple of 5 and 10 is 10. Convert -\frac{2}{5} and \frac{3}{10} to fractions with denominator 10.

$$0.1x-\frac{4}{10}-\frac{3}{10}=1$$

Since -\frac{4}{10} and \frac{3}{10} have the same denominator, subtract them by subtracting their numerators.

$$0.1x+\frac{-4-3}{10}=1$$

Subtract 3 from -4 to get -7.

$$0.1x-\frac{7}{10}=1$$

Add \frac{7}{10} to both sides.

$$0.1x=1+\frac{7}{10}$$

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

$$0.1x=\frac{10}{10}+\frac{7}{10}$$

Since \frac{10}{10} and \frac{7}{10} have the same denominator, add them by adding their numerators.

$$0.1x=\frac{10+7}{10}$$

Add 10 and 7 to get 17.

$$0.1x=\frac{17}{10}$$

Divide both sides by 0.1.

$$x=\frac{\frac{17}{10}}{0.1}$$

Express \frac{\frac{17}{10}}{0.1} as a single fraction.

$$x=\frac{17}{10\times 0.1}$$

Multiply 10 and 0.1 to get 1.

$$x=\frac{17}{1}$$

Divide 17 by 1 to get 17.

$$x=17$$