Solve 0.1*+3/0.2-0.4x-1/0.5=20

$$\frac { 0.1 * + 3 } { 0.2 } - \frac { 0.4 x - 1 } { 0.5 } = 20$$

Solve for x

$$x=-20.625$$

Steps for Solving Linear Equation

Multiply 0.1 and 3 to get 0.3.

$$\frac{0.3}{0.2}-\frac{0.4x-1}{0.5}=20$$

Expand \frac{0.3}{0.2} by multiplying both numerator and the denominator by 10.

$$\frac{3}{2}-\frac{0.4x-1}{0.5}=20$$

Divide each term of 0.4x-1 by 0.5 to get \frac{0.4x}{0.5}+\frac{-1}{0.5}.

$$\frac{3}{2}-\left(\frac{0.4x}{0.5}+\frac{-1}{0.5}\right)=20$$

Divide 0.4x by 0.5 to get 0.8x.

$$\frac{3}{2}-\left(0.8x+\frac{-1}{0.5}\right)=20$$

Expand \frac{-1}{0.5} by multiplying both numerator and the denominator by 10.

$$\frac{3}{2}-\left(0.8x+\frac{-10}{5}\right)=20$$

Divide -10 by 5 to get -2.

$$\frac{3}{2}-\left(0.8x-2\right)=20$$

To find the opposite of 0.8x-2, find the opposite of each term.

$$\frac{3}{2}-0.8x-\left(-2\right)=20$$

The opposite of -2 is 2.

$$\frac{3}{2}-0.8x+2=20$$

Convert 2 to fraction \frac{4}{2}.

$$\frac{3}{2}-0.8x+\frac{4}{2}=20$$

Since \frac{3}{2} and \frac{4}{2} have the same denominator, add them by adding their numerators.

$$\frac{3+4}{2}-0.8x=20$$

Add 3 and 4 to get 7.

$$\frac{7}{2}-0.8x=20$$

Subtract \frac{7}{2} from both sides.

$$-0.8x=20-\frac{7}{2}$$

Convert 20 to fraction \frac{40}{2}.

$$-0.8x=\frac{40}{2}-\frac{7}{2}$$

Since \frac{40}{2} and \frac{7}{2} have the same denominator, subtract them by subtracting their numerators.

$$-0.8x=\frac{40-7}{2}$$

Subtract 7 from 40 to get 33.

$$-0.8x=\frac{33}{2}$$

Divide both sides by -0.8.

$$x=\frac{\frac{33}{2}}{-0.8}$$

Express \frac{\frac{33}{2}}{-0.8} as a single fraction.

$$x=\frac{33}{2\left(-0.8\right)}$$

Multiply 2 and -0.8 to get -1.6.

$$x=\frac{33}{-1.6}$$

Expand \frac{33}{-1.6} by multiplying both numerator and the denominator by 10.

$$x=\frac{330}{-16}$$

Reduce the fraction \frac{330}{-16} to lowest terms by extracting and canceling out 2.

$$x=-\frac{165}{8}$$