Solve (1-x)-2*10^3(x-2)=10^3(2-x)

$$( 1 - x ) - 2 \cdot 10 ^ { 3 } ( x - 2 ) = 10 ^ { 3 } ( 2 - x )$$

Solve for x

$$x = \frac{2001}{1001} = 1\frac{1000}{1001} \approx 1.999000999$$

Steps for Solving Linear Equation

Calculate 10 to the power of 3 and get 1000.

$$1-x-2\times 1000\left(x-2\right)=10^{3}\left(2-x\right)$$

Multiply 2 and 1000 to get 2000.

$$1-x-2000\left(x-2\right)=10^{3}\left(2-x\right)$$

Use the distributive property to multiply -2000 by x-2.

$$1-x-2000x+4000=10^{3}\left(2-x\right)$$

Combine -x and -2000x to get -2001x.

$$1-2001x+4000=10^{3}\left(2-x\right)$$

Add 1 and 4000 to get 4001.

$$4001-2001x=10^{3}\left(2-x\right)$$

Calculate 10 to the power of 3 and get 1000.

$$4001-2001x=1000\left(2-x\right)$$

Use the distributive property to multiply 1000 by 2-x.

$$4001-2001x=2000-1000x$$

Add 1000x to both sides.

$$4001-2001x+1000x=2000$$

Combine -2001x and 1000x to get -1001x.

$$4001-1001x=2000$$

Subtract 4001 from both sides.

$$-1001x=2000-4001$$

Subtract 4001 from 2000 to get -2001.

$$-1001x=-2001$$

Divide both sides by -1001.

$$x=\frac{-2001}{-1001}$$

Fraction \frac{-2001}{-1001} can be simplified to \frac{2001}{1001} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{2001}{1001}$$