Solve 0.2x-3/0.1-2=x+2/3-0.8x/0.5

$$\frac { 0.2 x - 3 } { 0.1 } - 2 = \frac { x + 2 } { 3 } - \frac { 0.8 x } { 0.5 }$$

Solve for x

$$x=10$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3.

$$3\times \frac{0.2x-3}{0.1}-6=x+2-3\times \frac{0.8x}{0.5}$$

Divide 0.8x by 0.5 to get 1.6x.

$$3\times \frac{0.2x-3}{0.1}-6=x+2-3\times 1.6x$$

Multiply -3 and 1.6 to get -4.8.

$$3\times \frac{0.2x-3}{0.1}-6=x+2-4.8x$$

Combine x and -4.8x to get -3.8x.

$$3\times \frac{0.2x-3}{0.1}-6=-3.8x+2$$

Divide each term of 0.2x-3 by 0.1 to get \frac{0.2x}{0.1}+\frac{-3}{0.1}.

$$3\left(\frac{0.2x}{0.1}+\frac{-3}{0.1}\right)-6=-3.8x+2$$

Divide 0.2x by 0.1 to get 2x.

$$3\left(2x+\frac{-3}{0.1}\right)-6=-3.8x+2$$

Expand \frac{-3}{0.1} by multiplying both numerator and the denominator by 10. Anything divided by one gives itself.

$$3\left(2x-30\right)-6=-3.8x+2$$

Use the distributive property to multiply 3 by 2x-30.

$$6x-90-6=-3.8x+2$$

Subtract 6 from -90 to get -96.

$$6x-96=-3.8x+2$$

Add 3.8x to both sides.

$$6x-96+3.8x=2$$

Combine 6x and 3.8x to get 9.8x.

$$9.8x-96=2$$

Add 96 to both sides.

$$9.8x=2+96$$

Add 2 and 96 to get 98.

$$9.8x=98$$

Divide both sides by 9.8.

$$x=\frac{98}{9.8}$$

Expand \frac{98}{9.8} by multiplying both numerator and the denominator by 10.

$$x=\frac{980}{98}$$

Divide 980 by 98 to get 10.

$$x=10$$