Solve 0.4x+0.9/0.5-0.03-0.02x/0.03-x-5/2=0

$$\frac { 0.4 x + 0.9 } { 0.5 } - \frac { 0.03 - 0.02 x } { 0.03 } - \frac { x - 5 } { 2 } = 0$$

Solve for x

$$x = -\frac{99}{29} = -3\frac{12}{29} \approx -3.413793103$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$2\times \frac{0.4x+0.9}{0.5}-2\times \frac{0.03-0.02x}{0.03}-\left(x-5\right)=0$$

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

$$2\times \frac{0.4x+0.9}{0.5}-2\times \frac{0.03-0.02x}{0.03}-x-\left(-5\right)=0$$

The opposite of -5 is 5.

$$2\times \frac{0.4x+0.9}{0.5}-2\times \frac{0.03-0.02x}{0.03}-x+5=0$$

Divide each term of 0.4x+0.9 by 0.5 to get \frac{0.4x}{0.5}+\frac{0.9}{0.5}.

$$2\left(\frac{0.4x}{0.5}+\frac{0.9}{0.5}\right)-2\times \frac{0.03-0.02x}{0.03}-x+5=0$$

Divide 0.4x by 0.5 to get 0.8x.

$$2\left(0.8x+\frac{0.9}{0.5}\right)-2\times \frac{0.03-0.02x}{0.03}-x+5=0$$

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

$$2\left(0.8x+\frac{9}{5}\right)-2\times \frac{0.03-0.02x}{0.03}-x+5=0$$

Use the distributive property to multiply 2 by 0.8x+\frac{9}{5}.

$$1.6x+2\times \frac{9}{5}-2\times \frac{0.03-0.02x}{0.03}-x+5=0$$

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

$$1.6x+\frac{2\times 9}{5}-2\times \frac{0.03-0.02x}{0.03}-x+5=0$$

Multiply 2 and 9 to get 18.

$$1.6x+\frac{18}{5}-2\times \frac{0.03-0.02x}{0.03}-x+5=0$$

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

$$1.6x+\frac{18}{5}-2\left(\frac{0.03}{0.03}+\frac{-0.02x}{0.03}\right)-x+5=0$$

Divide 0.03 by 0.03 to get 1.

$$1.6x+\frac{18}{5}-2\left(1+\frac{-0.02x}{0.03}\right)-x+5=0$$

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

$$1.6x+\frac{18}{5}-2\left(1-\frac{2}{3}x\right)-x+5=0$$

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

$$1.6x+\frac{18}{5}-2+\frac{4}{3}x-x+5=0$$

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

$$1.6x+\frac{18}{5}-\frac{10}{5}+\frac{4}{3}x-x+5=0$$

Since \frac{18}{5} and \frac{10}{5} have the same denominator, subtract them by subtracting their numerators.

$$1.6x+\frac{18-10}{5}+\frac{4}{3}x-x+5=0$$

Subtract 10 from 18 to get 8.

$$1.6x+\frac{8}{5}+\frac{4}{3}x-x+5=0$$

Combine 1.6x and \frac{4}{3}x to get \frac{44}{15}x.

$$\frac{44}{15}x+\frac{8}{5}-x+5=0$$

Combine \frac{44}{15}x and -x to get \frac{29}{15}x.

$$\frac{29}{15}x+\frac{8}{5}+5=0$$

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

$$\frac{29}{15}x+\frac{8}{5}+\frac{25}{5}=0$$

Since \frac{8}{5} and \frac{25}{5} have the same denominator, add them by adding their numerators.

$$\frac{29}{15}x+\frac{8+25}{5}=0$$

Add 8 and 25 to get 33.

$$\frac{29}{15}x+\frac{33}{5}=0$$

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

$$\frac{29}{15}x=-\frac{33}{5}$$

Divide both sides by \frac{29}{15}.

$$x=\frac{-\frac{33}{5}}{\frac{29}{15}}$$

Express \frac{-\frac{33}{5}}{\frac{29}{15}} as a single fraction.

$$x=\frac{-33}{5\times \frac{29}{15}}$$

Multiply 5 and \frac{29}{15} to get \frac{29}{3}.

$$x=\frac{-33}{\frac{29}{3}}$$