Solve 4x-1.6/0.5-3x-5.4/0.2=1.8-x/0.1

$$\frac { 4 x - 1.6 } { 0.5 } - \frac { 3 x - 5.4 } { 0.2 } = \frac { 1.8 - x } { 0.1 }$$

Solve for x

$$x = -\frac{29}{15} = -1\frac{14}{15} \approx -1.933333333$$

Steps for Solving Linear Equation

Divide each term of 4x-1.6 by 0.5 to get \frac{4x}{0.5}+\frac{-1.6}{0.5}.

$$\frac{4x}{0.5}+\frac{-1.6}{0.5}-\frac{3x-5.4}{0.2}=\frac{1.8-x}{0.1}$$

Divide 4x by 0.5 to get 8x.

$$8x+\frac{-1.6}{0.5}-\frac{3x-5.4}{0.2}=\frac{1.8-x}{0.1}$$

Expand \frac{-1.6}{0.5} by multiplying both numerator and the denominator by 10.

$$8x+\frac{-16}{5}-\frac{3x-5.4}{0.2}=\frac{1.8-x}{0.1}$$

Fraction \frac{-16}{5} can be rewritten as -\frac{16}{5} by extracting the negative sign.

$$8x-\frac{16}{5}-\frac{3x-5.4}{0.2}=\frac{1.8-x}{0.1}$$

Divide each term of 3x-5.4 by 0.2 to get \frac{3x}{0.2}+\frac{-5.4}{0.2}.

$$8x-\frac{16}{5}-\left(\frac{3x}{0.2}+\frac{-5.4}{0.2}\right)=\frac{1.8-x}{0.1}$$

Divide 3x by 0.2 to get 15x.

$$8x-\frac{16}{5}-\left(15x+\frac{-5.4}{0.2}\right)=\frac{1.8-x}{0.1}$$

Expand \frac{-5.4}{0.2} by multiplying both numerator and the denominator by 10.

$$8x-\frac{16}{5}-\left(15x+\frac{-54}{2}\right)=\frac{1.8-x}{0.1}$$

Divide -54 by 2 to get -27.

$$8x-\frac{16}{5}-\left(15x-27\right)=\frac{1.8-x}{0.1}$$

To find the opposite of 15x-27, find the opposite of each term.

$$8x-\frac{16}{5}-15x-\left(-27\right)=\frac{1.8-x}{0.1}$$

The opposite of -27 is 27.

$$8x-\frac{16}{5}-15x+27=\frac{1.8-x}{0.1}$$

Combine 8x and -15x to get -7x.

$$-7x-\frac{16}{5}+27=\frac{1.8-x}{0.1}$$

Convert 27 to fraction \frac{135}{5}.

$$-7x-\frac{16}{5}+\frac{135}{5}=\frac{1.8-x}{0.1}$$

Since -\frac{16}{5} and \frac{135}{5} have the same denominator, add them by adding their numerators.

$$-7x+\frac{-16+135}{5}=\frac{1.8-x}{0.1}$$

Add -16 and 135 to get 119.

$$-7x+\frac{119}{5}=\frac{1.8-x}{0.1}$$

Divide each term of 1.8-x by 0.1 to get \frac{1.8}{0.1}+\frac{-x}{0.1}.

$$-7x+\frac{119}{5}=\frac{1.8}{0.1}+\frac{-x}{0.1}$$

Expand \frac{1.8}{0.1} by multiplying both numerator and the denominator by 10. Anything divided by one gives itself.

$$-7x+\frac{119}{5}=18+\frac{-x}{0.1}$$

Divide -x by 0.1 to get -10x.

$$-7x+\frac{119}{5}=18-10x$$

Add 10x to both sides.

$$-7x+\frac{119}{5}+10x=18$$

Combine -7x and 10x to get 3x.

$$3x+\frac{119}{5}=18$$

Subtract \frac{119}{5} from both sides.

$$3x=18-\frac{119}{5}$$

Convert 18 to fraction \frac{90}{5}.

$$3x=\frac{90}{5}-\frac{119}{5}$$

Since \frac{90}{5} and \frac{119}{5} have the same denominator, subtract them by subtracting their numerators.

$$3x=\frac{90-119}{5}$$

Subtract 119 from 90 to get -29.

$$3x=-\frac{29}{5}$$

Divide both sides by 3.

$$x=\frac{-\frac{29}{5}}{3}$$

Express \frac{-\frac{29}{5}}{3} as a single fraction.

$$x=\frac{-29}{5\times 3}$$

Multiply 5 and 3 to get 15.

$$x=\frac{-29}{15}$$

Fraction \frac{-29}{15} can be rewritten as -\frac{29}{15} by extracting the negative sign.

$$x=-\frac{29}{15}$$