Solve 0.04x+0.09/0.05-0.3x+0.2/0.3=x-5/2

$$\frac { 0.04 x + 0.09 } { 0.05 } - \frac { 0.3 x + 0.2 } { 0.3 } = \frac { x - 5 } { 2 }$$

Solve for x

$$x = \frac{109}{21} = 5\frac{4}{21} \approx 5.19047619$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$2\times \frac{0.04x+0.09}{0.05}-2\times \frac{0.3x+0.2}{0.3}=x-5$$

Divide each term of 0.04x+0.09 by 0.05 to get \frac{0.04x}{0.05}+\frac{0.09}{0.05}.

$$2\left(\frac{0.04x}{0.05}+\frac{0.09}{0.05}\right)-2\times \frac{0.3x+0.2}{0.3}=x-5$$

Divide 0.04x by 0.05 to get 0.8x.

$$2\left(0.8x+\frac{0.09}{0.05}\right)-2\times \frac{0.3x+0.2}{0.3}=x-5$$

Expand \frac{0.09}{0.05} by multiplying both numerator and the denominator by 100.

$$2\left(0.8x+\frac{9}{5}\right)-2\times \frac{0.3x+0.2}{0.3}=x-5$$

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

$$1.6x+2\times \frac{9}{5}-2\times \frac{0.3x+0.2}{0.3}=x-5$$

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

$$1.6x+\frac{2\times 9}{5}-2\times \frac{0.3x+0.2}{0.3}=x-5$$

Multiply 2 and 9 to get 18.

$$1.6x+\frac{18}{5}-2\times \frac{0.3x+0.2}{0.3}=x-5$$

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

$$1.6x+\frac{18}{5}-2\left(\frac{0.3x}{0.3}+\frac{0.2}{0.3}\right)=x-5$$

Cancel out 0.3 and 0.3.

$$1.6x+\frac{18}{5}-2\left(x+\frac{0.2}{0.3}\right)=x-5$$

Expand \frac{0.2}{0.3} by multiplying both numerator and the denominator by 10.

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

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

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

Express -2\times \frac{2}{3} as a single fraction.

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

Multiply -2 and 2 to get -4.

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

Fraction \frac{-4}{3} can be rewritten as -\frac{4}{3} by extracting the negative sign.

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

Combine 1.6x and -2x to get -0.4x.

$$-0.4x+\frac{18}{5}-\frac{4}{3}=x-5$$

Least common multiple of 5 and 3 is 15. Convert \frac{18}{5} and \frac{4}{3} to fractions with denominator 15.

$$-0.4x+\frac{54}{15}-\frac{20}{15}=x-5$$

Since \frac{54}{15} and \frac{20}{15} have the same denominator, subtract them by subtracting their numerators.

$$-0.4x+\frac{54-20}{15}=x-5$$

Subtract 20 from 54 to get 34.

$$-0.4x+\frac{34}{15}=x-5$$

Subtract x from both sides.

$$-0.4x+\frac{34}{15}-x=-5$$

Combine -0.4x and -x to get -1.4x.

$$-1.4x+\frac{34}{15}=-5$$

Subtract \frac{34}{15} from both sides.

$$-1.4x=-5-\frac{34}{15}$$

Convert -5 to fraction -\frac{75}{15}.

$$-1.4x=-\frac{75}{15}-\frac{34}{15}$$

Since -\frac{75}{15} and \frac{34}{15} have the same denominator, subtract them by subtracting their numerators.

$$-1.4x=\frac{-75-34}{15}$$

Subtract 34 from -75 to get -109.

$$-1.4x=-\frac{109}{15}$$

Divide both sides by -1.4.

$$x=\frac{-\frac{109}{15}}{-1.4}$$

Express \frac{-\frac{109}{15}}{-1.4} as a single fraction.

$$x=\frac{-109}{15\left(-1.4\right)}$$

Multiply 15 and -1.4 to get -21.

$$x=\frac{-109}{-21}$$

Fraction \frac{-109}{-21} can be simplified to \frac{109}{21} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{109}{21}$$