Solve 0.5(x-0.4)/0.35-0.6(x-2.71)/0.42=x+6.1

$$\frac { 0.5 ( x - 0.4 ) } { 0.35 } - \frac { 0.6 ( x - 2.71 ) } { 0.42 } = x + 6.1$$

Solve for x

$$x=-2.8$$

Steps for Solving Linear Equation

Use the distributive property to multiply 0.5 by x-0.4.

$$\frac{0.5x-0.2}{0.35}-\frac{0.6\left(x-2.71\right)}{0.42}=x+6.1$$

Use the distributive property to multiply 0.6 by x-2.71.

$$\frac{0.5x-0.2}{0.35}-\frac{0.6x-1.626}{0.42}=x+6.1$$

Divide each term of 0.5x-0.2 by 0.35 to get \frac{0.5x}{0.35}+\frac{-0.2}{0.35}.

$$\frac{0.5x}{0.35}+\frac{-0.2}{0.35}-\frac{0.6x-1.626}{0.42}=x+6.1$$

Divide 0.5x by 0.35 to get \frac{10}{7}x.

$$\frac{10}{7}x+\frac{-0.2}{0.35}-\frac{0.6x-1.626}{0.42}=x+6.1$$

Expand \frac{-0.2}{0.35} by multiplying both numerator and the denominator by 100.

$$\frac{10}{7}x+\frac{-20}{35}-\frac{0.6x-1.626}{0.42}=x+6.1$$

Reduce the fraction \frac{-20}{35} to lowest terms by extracting and canceling out 5.

$$\frac{10}{7}x-\frac{4}{7}-\frac{0.6x-1.626}{0.42}=x+6.1$$

Divide each term of 0.6x-1.626 by 0.42 to get \frac{0.6x}{0.42}+\frac{-1.626}{0.42}.

$$\frac{10}{7}x-\frac{4}{7}-\left(\frac{0.6x}{0.42}+\frac{-1.626}{0.42}\right)=x+6.1$$

Divide 0.6x by 0.42 to get \frac{10}{7}x.

$$\frac{10}{7}x-\frac{4}{7}-\left(\frac{10}{7}x+\frac{-1.626}{0.42}\right)=x+6.1$$

Expand \frac{-1.626}{0.42} by multiplying both numerator and the denominator by 1000.

$$\frac{10}{7}x-\frac{4}{7}-\left(\frac{10}{7}x+\frac{-1626}{420}\right)=x+6.1$$

Reduce the fraction \frac{-1626}{420} to lowest terms by extracting and canceling out 6.

$$\frac{10}{7}x-\frac{4}{7}-\left(\frac{10}{7}x-\frac{271}{70}\right)=x+6.1$$

To find the opposite of \frac{10}{7}x-\frac{271}{70}, find the opposite of each term.

$$\frac{10}{7}x-\frac{4}{7}-\frac{10}{7}x-\left(-\frac{271}{70}\right)=x+6.1$$

The opposite of -\frac{271}{70} is \frac{271}{70}.

$$\frac{10}{7}x-\frac{4}{7}-\frac{10}{7}x+\frac{271}{70}=x+6.1$$

Combine \frac{10}{7}x and -\frac{10}{7}x to get 0.

$$-\frac{4}{7}+\frac{271}{70}=x+6.1$$

Least common multiple of 7 and 70 is 70. Convert -\frac{4}{7} and \frac{271}{70} to fractions with denominator 70.

$$-\frac{40}{70}+\frac{271}{70}=x+6.1$$

Since -\frac{40}{70} and \frac{271}{70} have the same denominator, add them by adding their numerators.

$$\frac{-40+271}{70}=x+6.1$$

Add -40 and 271 to get 231.

$$\frac{231}{70}=x+6.1$$

Reduce the fraction \frac{231}{70} to lowest terms by extracting and canceling out 7.

$$\frac{33}{10}=x+6.1$$

Swap sides so that all variable terms are on the left hand side.

$$x+6.1=\frac{33}{10}$$

Subtract 6.1 from both sides.

$$x=\frac{33}{10}-6.1$$

Convert decimal number 6.1 to fraction \frac{61}{10}.

$$x=\frac{33}{10}-\frac{61}{10}$$

Since \frac{33}{10} and \frac{61}{10} have the same denominator, subtract them by subtracting their numerators.

$$x=\frac{33-61}{10}$$

Subtract 61 from 33 to get -28.

$$x=\frac{-28}{10}$$

Reduce the fraction \frac{-28}{10} to lowest terms by extracting and canceling out 2.

$$x=-\frac{14}{5}$$