Solve 0.2x-0.1/0.3=0.1x+0.4/0.05-1

$$\frac { 0.2 x - 0.1 } { 0.3 } = \frac { 0.1 x + 0.4 } { 0.05 } - 1$$

Solve for x

$$x=-5.5$$

Steps for Solving Linear Equation

Divide each term of 0.2x-0.1 by 0.3 to get \frac{0.2x}{0.3}+\frac{-0.1}{0.3}.

$$\frac{0.2x}{0.3}+\frac{-0.1}{0.3}=\frac{0.1x+0.4}{0.05}-1$$

Divide 0.2x by 0.3 to get \frac{2}{3}x.

$$\frac{2}{3}x+\frac{-0.1}{0.3}=\frac{0.1x+0.4}{0.05}-1$$

Expand \frac{-0.1}{0.3} by multiplying both numerator and the denominator by 10.

$$\frac{2}{3}x+\frac{-1}{3}=\frac{0.1x+0.4}{0.05}-1$$

Fraction \frac{-1}{3} can be rewritten as -\frac{1}{3} by extracting the negative sign.

$$\frac{2}{3}x-\frac{1}{3}=\frac{0.1x+0.4}{0.05}-1$$

Divide each term of 0.1x+0.4 by 0.05 to get \frac{0.1x}{0.05}+\frac{0.4}{0.05}.

$$\frac{2}{3}x-\frac{1}{3}=\frac{0.1x}{0.05}+\frac{0.4}{0.05}-1$$

Divide 0.1x by 0.05 to get 2x.

$$\frac{2}{3}x-\frac{1}{3}=2x+\frac{0.4}{0.05}-1$$

Expand \frac{0.4}{0.05} by multiplying both numerator and the denominator by 100.

$$\frac{2}{3}x-\frac{1}{3}=2x+\frac{40}{5}-1$$

Divide 40 by 5 to get 8.

$$\frac{2}{3}x-\frac{1}{3}=2x+8-1$$

Subtract 1 from 8 to get 7.

$$\frac{2}{3}x-\frac{1}{3}=2x+7$$

Subtract 2x from both sides.

$$\frac{2}{3}x-\frac{1}{3}-2x=7$$

Combine \frac{2}{3}x and -2x to get -\frac{4}{3}x.

$$-\frac{4}{3}x-\frac{1}{3}=7$$

Add \frac{1}{3} to both sides.

$$-\frac{4}{3}x=7+\frac{1}{3}$$

Convert 7 to fraction \frac{21}{3}.

$$-\frac{4}{3}x=\frac{21}{3}+\frac{1}{3}$$

Since \frac{21}{3} and \frac{1}{3} have the same denominator, add them by adding their numerators.

$$-\frac{4}{3}x=\frac{21+1}{3}$$

Add 21 and 1 to get 22.

$$-\frac{4}{3}x=\frac{22}{3}$$

Divide both sides by -\frac{4}{3}.

$$x=\frac{\frac{22}{3}}{-\frac{4}{3}}$$

Express \frac{\frac{22}{3}}{-\frac{4}{3}} as a single fraction.

$$x=\frac{22}{3\left(-\frac{4}{3}\right)}$$

Multiply 3 and -\frac{4}{3} to get -4.

$$x=\frac{22}{-4}$$

Reduce the fraction \frac{22}{-4} to lowest terms by extracting and canceling out 2.

$$x=-\frac{11}{2}$$