Solve 0.1x-0.4/1.2-1=0.2x+1/0.3

$$\frac { 0.1 x - 0.4 } { 1.2 } - 1 = \frac { 0.2 x + 1 } { 0.3 }$$

Solve for x

$$x=-8$$

Steps for Solving Linear Equation

Divide each term of 0.1x-0.4 by 1.2 to get \frac{0.1x}{1.2}+\frac{-0.4}{1.2}.

$$\frac{0.1x}{1.2}+\frac{-0.4}{1.2}-1=\frac{0.2x+1}{0.3}$$

Divide 0.1x by 1.2 to get \frac{1}{12}x.

$$\frac{1}{12}x+\frac{-0.4}{1.2}-1=\frac{0.2x+1}{0.3}$$

Expand \frac{-0.4}{1.2} by multiplying both numerator and the denominator by 10.

$$\frac{1}{12}x+\frac{-4}{12}-1=\frac{0.2x+1}{0.3}$$

Reduce the fraction \frac{-4}{12} to lowest terms by extracting and canceling out 4.

$$\frac{1}{12}x-\frac{1}{3}-1=\frac{0.2x+1}{0.3}$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{1}{12}x-\frac{1}{3}-\frac{3}{3}=\frac{0.2x+1}{0.3}$$

Since -\frac{1}{3} and \frac{3}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{12}x+\frac{-1-3}{3}=\frac{0.2x+1}{0.3}$$

Subtract 3 from -1 to get -4.

$$\frac{1}{12}x-\frac{4}{3}=\frac{0.2x+1}{0.3}$$

Divide each term of 0.2x+1 by 0.3 to get \frac{0.2x}{0.3}+\frac{1}{0.3}.

$$\frac{1}{12}x-\frac{4}{3}=\frac{0.2x}{0.3}+\frac{1}{0.3}$$

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

$$\frac{1}{12}x-\frac{4}{3}=\frac{2}{3}x+\frac{1}{0.3}$$

Expand \frac{1}{0.3} by multiplying both numerator and the denominator by 10.

$$\frac{1}{12}x-\frac{4}{3}=\frac{2}{3}x+\frac{10}{3}$$

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

$$\frac{1}{12}x-\frac{4}{3}-\frac{2}{3}x=\frac{10}{3}$$

Combine \frac{1}{12}x and -\frac{2}{3}x to get -\frac{7}{12}x.

$$-\frac{7}{12}x-\frac{4}{3}=\frac{10}{3}$$

Add \frac{4}{3} to both sides.

$$-\frac{7}{12}x=\frac{10}{3}+\frac{4}{3}$$

Since \frac{10}{3} and \frac{4}{3} have the same denominator, add them by adding their numerators.

$$-\frac{7}{12}x=\frac{10+4}{3}$$

Add 10 and 4 to get 14.

$$-\frac{7}{12}x=\frac{14}{3}$$

Divide both sides by -\frac{7}{12}.

$$x=\frac{\frac{14}{3}}{-\frac{7}{12}}$$

Express \frac{\frac{14}{3}}{-\frac{7}{12}} as a single fraction.

$$x=\frac{14}{3\left(-\frac{7}{12}\right)}$$

Multiply 3 and -\frac{7}{12} to get -1.75.

$$x=\frac{14}{-1.75}$$

Expand \frac{14}{-1.75} by multiplying both numerator and the denominator by 100.

$$x=\frac{1400}{-175}$$

Divide 1400 by -175 to get -8.

$$x=-8$$