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

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

Solve for x

$$x=-2.8$$

Steps for Solving Linear Equation

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

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

To find the opposite of x+6.1, find the opposite of each term.

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

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

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

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

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

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

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

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

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

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

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

Combine \frac{10}{7}x and -x to get \frac{3}{7}x.

$$\frac{3}{7}x-\frac{4}{7}-6.1=\frac{0.6x-1.626}{0.42}$$

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

$$\frac{3}{7}x-\frac{4}{7}-\frac{61}{10}=\frac{0.6x-1.626}{0.42}$$

Least common multiple of 7 and 10 is 70. Convert -\frac{4}{7} and \frac{61}{10} to fractions with denominator 70.

$$\frac{3}{7}x-\frac{40}{70}-\frac{427}{70}=\frac{0.6x-1.626}{0.42}$$

Since -\frac{40}{70} and \frac{427}{70} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{7}x+\frac{-40-427}{70}=\frac{0.6x-1.626}{0.42}$$

Subtract 427 from -40 to get -467.

$$\frac{3}{7}x-\frac{467}{70}=\frac{0.6x-1.626}{0.42}$$

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

$$\frac{3}{7}x-\frac{467}{70}=\frac{0.6x}{0.42}+\frac{-1.626}{0.42}$$

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

$$\frac{3}{7}x-\frac{467}{70}=\frac{10}{7}x+\frac{-1.626}{0.42}$$

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

$$\frac{3}{7}x-\frac{467}{70}=\frac{10}{7}x+\frac{-1626}{420}$$

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

$$\frac{3}{7}x-\frac{467}{70}=\frac{10}{7}x-\frac{271}{70}$$

Subtract \frac{10}{7}x from both sides.

$$\frac{3}{7}x-\frac{467}{70}-\frac{10}{7}x=-\frac{271}{70}$$

Combine \frac{3}{7}x and -\frac{10}{7}x to get -x.

$$-x-\frac{467}{70}=-\frac{271}{70}$$

Add \frac{467}{70} to both sides.

$$-x=-\frac{271}{70}+\frac{467}{70}$$

Since -\frac{271}{70} and \frac{467}{70} have the same denominator, add them by adding their numerators.

$$-x=\frac{-271+467}{70}$$

Add -271 and 467 to get 196.

$$-x=\frac{196}{70}$$

Reduce the fraction \frac{196}{70} to lowest terms by extracting and canceling out 14.

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

Multiply both sides by -1.

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