Solve 0.9x-0.5x-200=0.9x*0.2%

$$0.9x-0.5x-200 = 0.9x \times 0.2 \%$$

Solve for x

$$x = \frac{1000000}{1991} = 502\frac{518}{1991} \approx 502.260170768$$

Steps for Solving Linear Equation

Combine 0.9x and -0.5x to get 0.4x.

$$0.4x-200=0.9x\times \frac{0.2}{100}$$

Expand \frac{0.2}{100} by multiplying both numerator and the denominator by 10.

$$0.4x-200=0.9x\times \frac{2}{1000}$$

Reduce the fraction \frac{2}{1000} to lowest terms by extracting and canceling out 2.

$$0.4x-200=0.9x\times \frac{1}{500}$$

Convert decimal number 0.9 to fraction \frac{9}{10}.

$$0.4x-200=\frac{9}{10}x\times \frac{1}{500}$$

Multiply \frac{9}{10} times \frac{1}{500} by multiplying numerator times numerator and denominator times denominator.

$$0.4x-200=\frac{9\times 1}{10\times 500}x$$

Do the multiplications in the fraction \frac{9\times 1}{10\times 500}.

$$0.4x-200=\frac{9}{5000}x$$

Subtract \frac{9}{5000}x from both sides.

$$0.4x-200-\frac{9}{5000}x=0$$

Combine 0.4x and -\frac{9}{5000}x to get \frac{1991}{5000}x.

$$\frac{1991}{5000}x-200=0$$

Add 200 to both sides. Anything plus zero gives itself.

$$\frac{1991}{5000}x=200$$

Multiply both sides by \frac{5000}{1991}, the reciprocal of \frac{1991}{5000}.

$$x=200\times \frac{5000}{1991}$$

Express 200\times \frac{5000}{1991} as a single fraction.

$$x=\frac{200\times 5000}{1991}$$

Multiply 200 and 5000 to get 1000000.

$$x=\frac{1000000}{1991}$$