Solve 6000*75%(x-1)+6000<6000*80%x

$$6000 \times 75 \% (x-1)+6000 < 6000 \times 80 \% x$$

Solve for x

$$x>5$$

Solution Steps

Reduce the fraction \frac{75}{100} to lowest terms by extracting and canceling out 25.

$$6000\times \frac{3}{4}\left(x-1\right)+6000<6000\times \frac{80}{100}x$$

Express 6000\times \frac{3}{4} as a single fraction.

$$\frac{6000\times 3}{4}\left(x-1\right)+6000<6000\times \frac{80}{100}x$$

Multiply 6000 and 3 to get 18000.

$$\frac{18000}{4}\left(x-1\right)+6000<6000\times \frac{80}{100}x$$

Divide 18000 by 4 to get 4500.

$$4500\left(x-1\right)+6000<6000\times \frac{80}{100}x$$

Use the distributive property to multiply 4500 by x-1.

$$4500x-4500+6000<6000\times \frac{80}{100}x$$

Add -4500 and 6000 to get 1500.

$$4500x+1500<6000\times \frac{80}{100}x$$

Reduce the fraction \frac{80}{100} to lowest terms by extracting and canceling out 20.

$$4500x+1500<6000\times \frac{4}{5}x$$

Express 6000\times \frac{4}{5} as a single fraction.

$$4500x+1500<\frac{6000\times 4}{5}x$$

Multiply 6000 and 4 to get 24000.

$$4500x+1500<\frac{24000}{5}x$$

Divide 24000 by 5 to get 4800.

$$4500x+1500<4800x$$

Subtract 4800x from both sides.

$$4500x+1500-4800x<0$$

Combine 4500x and -4800x to get -300x.

$$-300x+1500<0$$

Subtract 1500 from both sides. Anything subtracted from zero gives its negation.

$$-300x<-1500$$

Divide both sides by -300. Since -300 is negative, the inequality direction is changed.

$$x>\frac{-1500}{-300}$$

Divide -1500 by -300 to get 5.

$$x>5$$