Solve 1.8-8x/1.2-1.3-3x/2=5x-0.4/0.3

$$\frac{ 1.8-8x }{ 1.2 } - \frac{ 1.3-3x }{ 2 } = \frac{ 5x-0.4 }{ 0.3 }$$

Solve for x

$$x=0.1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$2\times \frac{1.8-8x}{1.2}-\left(1.3-3x\right)=2\times \frac{5x-0.4}{0.3}$$

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

$$2\times \frac{1.8-8x}{1.2}-1.3-\left(-3x\right)=2\times \frac{5x-0.4}{0.3}$$

The opposite of -3x is 3x.

$$2\times \frac{1.8-8x}{1.2}-1.3+3x=2\times \frac{5x-0.4}{0.3}$$

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

$$2\left(\frac{1.8}{1.2}+\frac{-8x}{1.2}\right)-1.3+3x=2\times \frac{5x-0.4}{0.3}$$

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

$$2\left(\frac{18}{12}+\frac{-8x}{1.2}\right)-1.3+3x=2\times \frac{5x-0.4}{0.3}$$

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

$$2\left(\frac{3}{2}+\frac{-8x}{1.2}\right)-1.3+3x=2\times \frac{5x-0.4}{0.3}$$

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

$$2\left(\frac{3}{2}-\frac{20}{3}x\right)-1.3+3x=2\times \frac{5x-0.4}{0.3}$$

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

$$2\times \frac{3}{2}-\frac{40}{3}x-1.3+3x=2\times \frac{5x-0.4}{0.3}$$

Cancel out 2 and 2.

$$3-\frac{40}{3}x-1.3+3x=2\times \frac{5x-0.4}{0.3}$$

Subtract 1.3 from 3 to get 1.7.

$$1.7-\frac{40}{3}x+3x=2\times \frac{5x-0.4}{0.3}$$

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

$$1.7-\frac{31}{3}x=2\times \frac{5x-0.4}{0.3}$$

Divide each term of 5x-0.4 by 0.3 to get \frac{5x}{0.3}+\frac{-0.4}{0.3}.

$$1.7-\frac{31}{3}x=2\left(\frac{5x}{0.3}+\frac{-0.4}{0.3}\right)$$

Divide 5x by 0.3 to get \frac{50}{3}x.

$$1.7-\frac{31}{3}x=2\left(\frac{50}{3}x+\frac{-0.4}{0.3}\right)$$

Expand \frac{-0.4}{0.3} by multiplying both numerator and the denominator by 10.

$$1.7-\frac{31}{3}x=2\left(\frac{50}{3}x+\frac{-4}{3}\right)$$

Fraction \frac{-4}{3} can be rewritten as -\frac{4}{3} by extracting the negative sign.

$$1.7-\frac{31}{3}x=2\left(\frac{50}{3}x-\frac{4}{3}\right)$$

Use the distributive property to multiply 2 by \frac{50}{3}x-\frac{4}{3}.

$$1.7-\frac{31}{3}x=\frac{100}{3}x+2\left(-\frac{4}{3}\right)$$

Express 2\left(-\frac{4}{3}\right) as a single fraction.

$$1.7-\frac{31}{3}x=\frac{100}{3}x+\frac{2\left(-4\right)}{3}$$

Multiply 2 and -4 to get -8.

$$1.7-\frac{31}{3}x=\frac{100}{3}x+\frac{-8}{3}$$

Fraction \frac{-8}{3} can be rewritten as -\frac{8}{3} by extracting the negative sign.

$$1.7-\frac{31}{3}x=\frac{100}{3}x-\frac{8}{3}$$

Subtract \frac{100}{3}x from both sides.

$$1.7-\frac{31}{3}x-\frac{100}{3}x=-\frac{8}{3}$$

Combine -\frac{31}{3}x and -\frac{100}{3}x to get -\frac{131}{3}x.

$$1.7-\frac{131}{3}x=-\frac{8}{3}$$

Subtract 1.7 from both sides.

$$-\frac{131}{3}x=-\frac{8}{3}-1.7$$

Convert decimal number 1.7 to fraction \frac{17}{10}.

$$-\frac{131}{3}x=-\frac{8}{3}-\frac{17}{10}$$

Least common multiple of 3 and 10 is 30. Convert -\frac{8}{3} and \frac{17}{10} to fractions with denominator 30.

$$-\frac{131}{3}x=-\frac{80}{30}-\frac{51}{30}$$

Since -\frac{80}{30} and \frac{51}{30} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{131}{3}x=\frac{-80-51}{30}$$

Subtract 51 from -80 to get -131.

$$-\frac{131}{3}x=-\frac{131}{30}$$

Divide both sides by -\frac{131}{3}.

$$x=\frac{-\frac{131}{30}}{-\frac{131}{3}}$$

Express \frac{-\frac{131}{30}}{-\frac{131}{3}} as a single fraction.

$$x=\frac{-131}{30\left(-\frac{131}{3}\right)}$$

Multiply 30 and -\frac{131}{3} to get -1310.

$$x=\frac{-131}{-1310}$$

Reduce the fraction \frac{-131}{-1310} to lowest terms by extracting and canceling out -131.

$$x=\frac{1}{10}$$