Solve 0.05+0.02x/0.03-1-0.3x/0.2=1

$$\frac { 0.05 + 0.02 x } { 0.03 } - \frac { 1 - 0.3 x } { 0.2 } = 1$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

Divide each term of 0.05+0.02x by 0.03 to get \frac{0.05}{0.03}+\frac{0.02x}{0.03}.

$$\frac{0.05}{0.03}+\frac{0.02x}{0.03}-\frac{1-0.3x}{0.2}=1$$

Expand \frac{0.05}{0.03} by multiplying both numerator and the denominator by 100.

$$\frac{5}{3}+\frac{0.02x}{0.03}-\frac{1-0.3x}{0.2}=1$$

Divide 0.02x by 0.03 to get \frac{2}{3}x.

$$\frac{5}{3}+\frac{2}{3}x-\frac{1-0.3x}{0.2}=1$$

Divide each term of 1-0.3x by 0.2 to get \frac{1}{0.2}+\frac{-0.3x}{0.2}.

$$\frac{5}{3}+\frac{2}{3}x-\left(\frac{1}{0.2}+\frac{-0.3x}{0.2}\right)=1$$

Expand \frac{1}{0.2} by multiplying both numerator and the denominator by 10.

$$\frac{5}{3}+\frac{2}{3}x-\left(\frac{10}{2}+\frac{-0.3x}{0.2}\right)=1$$

Divide 10 by 2 to get 5.

$$\frac{5}{3}+\frac{2}{3}x-\left(5+\frac{-0.3x}{0.2}\right)=1$$

Divide -0.3x by 0.2 to get -1.5x.

$$\frac{5}{3}+\frac{2}{3}x-\left(5-1.5x\right)=1$$

To find the opposite of 5-1.5x, find the opposite of each term.

$$\frac{5}{3}+\frac{2}{3}x-5-\left(-1.5x\right)=1$$

The opposite of -1.5x is 1.5x.

$$\frac{5}{3}+\frac{2}{3}x-5+1.5x=1$$

Convert 5 to fraction \frac{15}{3}.

$$\frac{5}{3}+\frac{2}{3}x-\frac{15}{3}+1.5x=1$$

Since \frac{5}{3} and \frac{15}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5-15}{3}+\frac{2}{3}x+1.5x=1$$

Subtract 15 from 5 to get -10.

$$-\frac{10}{3}+\frac{2}{3}x+1.5x=1$$

Combine \frac{2}{3}x and 1.5x to get \frac{13}{6}x.

$$-\frac{10}{3}+\frac{13}{6}x=1$$

Add \frac{10}{3} to both sides.

$$\frac{13}{6}x=1+\frac{10}{3}$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{13}{6}x=\frac{3}{3}+\frac{10}{3}$$

Since \frac{3}{3} and \frac{10}{3} have the same denominator, add them by adding their numerators.

$$\frac{13}{6}x=\frac{3+10}{3}$$

Add 3 and 10 to get 13.

$$\frac{13}{6}x=\frac{13}{3}$$

Divide both sides by \frac{13}{6}.

$$x=\frac{\frac{13}{3}}{\frac{13}{6}}$$

Express \frac{\frac{13}{3}}{\frac{13}{6}} as a single fraction.

$$x=\frac{13}{3\times \frac{13}{6}}$$

Multiply 3 and \frac{13}{6} to get 6.5.

$$x=\frac{13}{6.5}$$

Expand \frac{13}{6.5} by multiplying both numerator and the denominator by 10.

$$x=\frac{130}{65}$$

Divide 130 by 65 to get 2.

$$x=2$$