Solve 0.3x+0.9/0.5-x-5/2-0.03+0.02x/0.03=0

$$\frac{ 0.3x+0.9 }{ 0.5 } - \frac{ x-5 }{ 2 } - \frac{ 0.03+0.02x }{ 0.03 } =0$$

Solve for x

$$x = \frac{99}{17} = 5\frac{14}{17} \approx 5.823529412$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$2\times \frac{0.3x+0.9}{0.5}-\left(x-5\right)-2\times \frac{0.03+0.02x}{0.03}=0$$

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

$$2\times \frac{0.3x+0.9}{0.5}-x-\left(-5\right)-2\times \frac{0.03+0.02x}{0.03}=0$$

The opposite of -5 is 5.

$$2\times \frac{0.3x+0.9}{0.5}-x+5-2\times \frac{0.03+0.02x}{0.03}=0$$

Divide each term of 0.3x+0.9 by 0.5 to get \frac{0.3x}{0.5}+\frac{0.9}{0.5}.

$$2\left(\frac{0.3x}{0.5}+\frac{0.9}{0.5}\right)-x+5-2\times \frac{0.03+0.02x}{0.03}=0$$

Divide 0.3x by 0.5 to get 0.6x.

$$2\left(0.6x+\frac{0.9}{0.5}\right)-x+5-2\times \frac{0.03+0.02x}{0.03}=0$$

Expand \frac{0.9}{0.5} by multiplying both numerator and the denominator by 10.

$$2\left(0.6x+\frac{9}{5}\right)-x+5-2\times \frac{0.03+0.02x}{0.03}=0$$

Use the distributive property to multiply 2 by 0.6x+\frac{9}{5}.

$$1.2x+2\times \frac{9}{5}-x+5-2\times \frac{0.03+0.02x}{0.03}=0$$

Express 2\times \frac{9}{5} as a single fraction.

$$1.2x+\frac{2\times 9}{5}-x+5-2\times \frac{0.03+0.02x}{0.03}=0$$

Multiply 2 and 9 to get 18.

$$1.2x+\frac{18}{5}-x+5-2\times \frac{0.03+0.02x}{0.03}=0$$

Combine 1.2x and -x to get 0.2x.

$$0.2x+\frac{18}{5}+5-2\times \frac{0.03+0.02x}{0.03}=0$$

Convert 5 to fraction \frac{25}{5}.

$$0.2x+\frac{18}{5}+\frac{25}{5}-2\times \frac{0.03+0.02x}{0.03}=0$$

Since \frac{18}{5} and \frac{25}{5} have the same denominator, add them by adding their numerators.

$$0.2x+\frac{18+25}{5}-2\times \frac{0.03+0.02x}{0.03}=0$$

Add 18 and 25 to get 43.

$$0.2x+\frac{43}{5}-2\times \frac{0.03+0.02x}{0.03}=0$$

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

$$0.2x+\frac{43}{5}-2\left(\frac{0.03}{0.03}+\frac{0.02x}{0.03}\right)=0$$

Divide 0.03 by 0.03 to get 1.

$$0.2x+\frac{43}{5}-2\left(1+\frac{0.02x}{0.03}\right)=0$$

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

$$0.2x+\frac{43}{5}-2\left(1+\frac{2}{3}x\right)=0$$

Use the distributive property to multiply -2 by 1+\frac{2}{3}x.

$$0.2x+\frac{43}{5}-2-\frac{4}{3}x=0$$

Convert 2 to fraction \frac{10}{5}.

$$0.2x+\frac{43}{5}-\frac{10}{5}-\frac{4}{3}x=0$$

Since \frac{43}{5} and \frac{10}{5} have the same denominator, subtract them by subtracting their numerators.

$$0.2x+\frac{43-10}{5}-\frac{4}{3}x=0$$

Subtract 10 from 43 to get 33.

$$0.2x+\frac{33}{5}-\frac{4}{3}x=0$$

Combine 0.2x and -\frac{4}{3}x to get -\frac{17}{15}x.

$$-\frac{17}{15}x+\frac{33}{5}=0$$

Subtract \frac{33}{5} from both sides. Anything subtracted from zero gives its negation.

$$-\frac{17}{15}x=-\frac{33}{5}$$

Divide both sides by -\frac{17}{15}.

$$x=\frac{-\frac{33}{5}}{-\frac{17}{15}}$$

Express \frac{-\frac{33}{5}}{-\frac{17}{15}} as a single fraction.

$$x=\frac{-33}{5\left(-\frac{17}{15}\right)}$$

Multiply 5 and -\frac{17}{15} to get -\frac{17}{3}.

$$x=\frac{-33}{-\frac{17}{3}}$$