Solve 6000+(1-2300)*6000(x-1)<(1-2006)*6000x

$$6000 + ( 1 - 2300 ) \times 6000 ( x - 1 ) < ( 1 - 2006 ) \times 6000 x$$

Solve for x

$$x>\frac{1150}{147}$$

Solution Steps

Subtract 2300 from 1 to get -2299.

$$6000-2299\times 6000\left(x-1\right)<\left(1-2006\right)\times 6000x$$

Multiply -2299 and 6000 to get -13794000.

$$6000-13794000\left(x-1\right)<\left(1-2006\right)\times 6000x$$

Use the distributive property to multiply -13794000 by x-1.

$$6000-13794000x+13794000<\left(1-2006\right)\times 6000x$$

Add 6000 and 13794000 to get 13800000.

$$13800000-13794000x<\left(1-2006\right)\times 6000x$$

Subtract 2006 from 1 to get -2005.

$$13800000-13794000x<-2005\times 6000x$$

Multiply -2005 and 6000 to get -12030000.

$$13800000-13794000x<-12030000x$$

Add 12030000x to both sides.

$$13800000-13794000x+12030000x<0$$

Combine -13794000x and 12030000x to get -1764000x.

$$13800000-1764000x<0$$

Subtract 13800000 from both sides. Anything subtracted from zero gives its negation.

$$-1764000x<-13800000$$

Divide both sides by -1764000. Since -1764000 is negative, the inequality direction is changed.

$$x>\frac{-13800000}{-1764000}$$

Reduce the fraction \frac{-13800000}{-1764000} to lowest terms by extracting and canceling out -12000.

$$x>\frac{1150}{147}$$