Solve 0.5x-0.1/0.2-0.5=0.4x-0.6/1.2

$$\frac{ 0.5x-0.1 }{ 0.2 } -0.5 = \frac{ 0.4x-0.6 }{ 1.2 }$$

Solve for x

$$x=\frac{3}{13}\approx 0.230769231$$

Steps for Solving Linear Equation

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

$$\frac{0.5x}{0.2}+\frac{-0.1}{0.2}-0.5=\frac{0.4x-0.6}{1.2}$$

Divide 0.5x by 0.2 to get 2.5x.

$$2.5x+\frac{-0.1}{0.2}-0.5=\frac{0.4x-0.6}{1.2}$$

Expand \frac{-0.1}{0.2} by multiplying both numerator and the denominator by 10.

$$2.5x+\frac{-1}{2}-0.5=\frac{0.4x-0.6}{1.2}$$

Fraction \frac{-1}{2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

$$2.5x-\frac{1}{2}-0.5=\frac{0.4x-0.6}{1.2}$$

Convert decimal number 0.5 to fraction \frac{5}{10}. Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$2.5x-\frac{1}{2}-\frac{1}{2}=\frac{0.4x-0.6}{1.2}$$

Since -\frac{1}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$2.5x+\frac{-1-1}{2}=\frac{0.4x-0.6}{1.2}$$

Subtract 1 from -1 to get -2.

$$2.5x+\frac{-2}{2}=\frac{0.4x-0.6}{1.2}$$

Divide -2 by 2 to get -1.

$$2.5x-1=\frac{0.4x-0.6}{1.2}$$

Divide each term of 0.4x-0.6 by 1.2 to get \frac{0.4x}{1.2}+\frac{-0.6}{1.2}.

$$2.5x-1=\frac{0.4x}{1.2}+\frac{-0.6}{1.2}$$

Divide 0.4x by 1.2 to get \frac{1}{3}x.

$$2.5x-1=\frac{1}{3}x+\frac{-0.6}{1.2}$$

Expand \frac{-0.6}{1.2} by multiplying both numerator and the denominator by 10.

$$2.5x-1=\frac{1}{3}x+\frac{-6}{12}$$

Reduce the fraction \frac{-6}{12} to lowest terms by extracting and canceling out 6.

$$2.5x-1=\frac{1}{3}x-\frac{1}{2}$$

Subtract \frac{1}{3}x from both sides.

$$2.5x-1-\frac{1}{3}x=-\frac{1}{2}$$

Combine 2.5x and -\frac{1}{3}x to get \frac{13}{6}x.

$$\frac{13}{6}x-1=-\frac{1}{2}$$

Add 1 to both sides.

$$\frac{13}{6}x=-\frac{1}{2}+1$$

Convert 1 to fraction \frac{2}{2}.

$$\frac{13}{6}x=-\frac{1}{2}+\frac{2}{2}$$

Since -\frac{1}{2} and \frac{2}{2} have the same denominator, add them by adding their numerators.

$$\frac{13}{6}x=\frac{-1+2}{2}$$

Add -1 and 2 to get 1.

$$\frac{13}{6}x=\frac{1}{2}$$

Divide both sides by \frac{13}{6}.

$$x=\frac{\frac{1}{2}}{\frac{13}{6}}$$

Express \frac{\frac{1}{2}}{\frac{13}{6}} as a single fraction.

$$x=\frac{1}{2\times \frac{13}{6}}$$

Multiply 2 and \frac{13}{6} to get \frac{13}{3}.

$$x=\frac{1}{\frac{13}{3}}$$