Solve 1.3x/0.3-1.5-x/0.2=0.5

$$\frac{ 1.3x }{ 0.3 } - \frac{ 1.5-x }{ 0.2 } =0.5$$

Solve for x

$$x=\frac{6}{7}\approx 0.857142857$$

Steps for Solving Linear Equation

Divide 1.3x by 0.3 to get \frac{13}{3}x.

$$\frac{13}{3}x-\frac{1.5-x}{0.2}=0.5$$

Divide each term of 1.5-x by 0.2 to get \frac{1.5}{0.2}+\frac{-x}{0.2}.

$$\frac{13}{3}x-\left(\frac{1.5}{0.2}+\frac{-x}{0.2}\right)=0.5$$

Expand \frac{1.5}{0.2} by multiplying both numerator and the denominator by 10.

$$\frac{13}{3}x-\left(\frac{15}{2}+\frac{-x}{0.2}\right)=0.5$$

Divide -x by 0.2 to get -5x.

$$\frac{13}{3}x-\left(\frac{15}{2}-5x\right)=0.5$$

To find the opposite of \frac{15}{2}-5x, find the opposite of each term.

$$\frac{13}{3}x-\frac{15}{2}-\left(-5x\right)=0.5$$

The opposite of -5x is 5x.

$$\frac{13}{3}x-\frac{15}{2}+5x=0.5$$

Combine \frac{13}{3}x and 5x to get \frac{28}{3}x.

$$\frac{28}{3}x-\frac{15}{2}=0.5$$

Add \frac{15}{2} to both sides.

$$\frac{28}{3}x=0.5+\frac{15}{2}$$

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.

$$\frac{28}{3}x=\frac{1}{2}+\frac{15}{2}$$

Since \frac{1}{2} and \frac{15}{2} have the same denominator, add them by adding their numerators.

$$\frac{28}{3}x=\frac{1+15}{2}$$

Add 1 and 15 to get 16.

$$\frac{28}{3}x=\frac{16}{2}$$

Divide 16 by 2 to get 8.

$$\frac{28}{3}x=8$$

Divide both sides by \frac{28}{3}.

$$x=\frac{8}{\frac{28}{3}}$$