Solve 1.8-8x/1.2-1.3-3x/2=5x-0.4/0.2+2

$$\frac { 1.8 - 8 x } { 1.2 } - \frac { 1.3 - 3 x } { 2 } = \frac { 5 x - 0.4 } { 0.2 } + 2$$

Solve for x

$$x=\frac{51}{1810}\approx 0.028176796$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$2\times \frac{1.8-8x}{1.2}-\left(1.3-3x\right)=2\times \frac{5x-0.4}{0.2}+4$$

To find the opposite of 1.3-3x, find the opposite of each term.

$$2\times \frac{1.8-8x}{1.2}-1.3-\left(-3x\right)=2\times \frac{5x-0.4}{0.2}+4$$

The opposite of -3x is 3x.

$$2\times \frac{1.8-8x}{1.2}-1.3+3x=2\times \frac{5x-0.4}{0.2}+4$$

Divide each term of 1.8-8x by 1.2 to get \frac{1.8}{1.2}+\frac{-8x}{1.2}.

$$2\left(\frac{1.8}{1.2}+\frac{-8x}{1.2}\right)-1.3+3x=2\times \frac{5x-0.4}{0.2}+4$$

Expand \frac{1.8}{1.2} by multiplying both numerator and the denominator by 10.

$$2\left(\frac{18}{12}+\frac{-8x}{1.2}\right)-1.3+3x=2\times \frac{5x-0.4}{0.2}+4$$

Reduce the fraction \frac{18}{12} to lowest terms by extracting and canceling out 6.

$$2\left(\frac{3}{2}+\frac{-8x}{1.2}\right)-1.3+3x=2\times \frac{5x-0.4}{0.2}+4$$

Divide -8x by 1.2 to get -\frac{20}{3}x.

$$2\left(\frac{3}{2}-\frac{20}{3}x\right)-1.3+3x=2\times \frac{5x-0.4}{0.2}+4$$

Use the distributive property to multiply 2 by \frac{3}{2}-\frac{20}{3}x.

$$2\times \frac{3}{2}-\frac{40}{3}x-1.3+3x=2\times \frac{5x-0.4}{0.2}+4$$

Cancel out 2 and 2.

$$3-\frac{40}{3}x-1.3+3x=2\times \frac{5x-0.4}{0.2}+4$$

Subtract 1.3 from 3 to get 1.7.

$$1.7-\frac{40}{3}x+3x=2\times \frac{5x-0.4}{0.2}+4$$

Combine -\frac{40}{3}x and 3x to get -\frac{31}{3}x.

$$1.7-\frac{31}{3}x=2\times \frac{5x-0.4}{0.2}+4$$

Divide each term of 5x-0.4 by 0.2 to get \frac{5x}{0.2}+\frac{-0.4}{0.2}.

$$1.7-\frac{31}{3}x=2\left(\frac{5x}{0.2}+\frac{-0.4}{0.2}\right)+4$$

Divide 5x by 0.2 to get 25x.

$$1.7-\frac{31}{3}x=2\left(25x+\frac{-0.4}{0.2}\right)+4$$

Expand \frac{-0.4}{0.2} by multiplying both numerator and the denominator by 10.

$$1.7-\frac{31}{3}x=2\left(25x+\frac{-4}{2}\right)+4$$

Divide -4 by 2 to get -2.

$$1.7-\frac{31}{3}x=2\left(25x-2\right)+4$$

Use the distributive property to multiply 2 by 25x-2.

$$1.7-\frac{31}{3}x=50x-4+4$$

Add -4 and 4 to get 0.

$$1.7-\frac{31}{3}x=50x$$

Subtract 50x from both sides.

$$1.7-\frac{31}{3}x-50x=0$$

Combine -\frac{31}{3}x and -50x to get -\frac{181}{3}x.

$$1.7-\frac{181}{3}x=0$$

Subtract 1.7 from both sides. Anything subtracted from zero gives its negation.

$$-\frac{181}{3}x=-1.7$$

Divide both sides by -\frac{181}{3}.

$$x=\frac{-1.7}{-\frac{181}{3}}$$