Solve 6000+(1-25%)*6000(x-1)<(1-20%)*6000x

$$6000 + ( 1 - 25 \% ) \times 6000 ( x - 1 ) < ( 1 - 20 \% ) \times 6000 x$$

Solve for x

$$x>5$$

Solution Steps

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

$$6000+\left(1-\frac{1}{4}\right)\times 6000\left(x-1\right)<\left(1-\frac{20}{100}\right)\times 6000x$$

Convert 1 to fraction \frac{4}{4}.

$$6000+\left(\frac{4}{4}-\frac{1}{4}\right)\times 6000\left(x-1\right)<\left(1-\frac{20}{100}\right)\times 6000x$$

Since \frac{4}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$6000+\frac{4-1}{4}\times 6000\left(x-1\right)<\left(1-\frac{20}{100}\right)\times 6000x$$

Subtract 1 from 4 to get 3.

$$6000+\frac{3}{4}\times 6000\left(x-1\right)<\left(1-\frac{20}{100}\right)\times 6000x$$

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

$$6000+\frac{3\times 6000}{4}\left(x-1\right)<\left(1-\frac{20}{100}\right)\times 6000x$$

Multiply 3 and 6000 to get 18000.

$$6000+\frac{18000}{4}\left(x-1\right)<\left(1-\frac{20}{100}\right)\times 6000x$$

Divide 18000 by 4 to get 4500.

$$6000+4500\left(x-1\right)<\left(1-\frac{20}{100}\right)\times 6000x$$

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

$$6000+4500x-4500<\left(1-\frac{20}{100}\right)\times 6000x$$

Subtract 4500 from 6000 to get 1500.

$$1500+4500x<\left(1-\frac{20}{100}\right)\times 6000x$$

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

$$1500+4500x<\left(1-\frac{1}{5}\right)\times 6000x$$

Convert 1 to fraction \frac{5}{5}.

$$1500+4500x<\left(\frac{5}{5}-\frac{1}{5}\right)\times 6000x$$

Since \frac{5}{5} and \frac{1}{5} have the same denominator, subtract them by subtracting their numerators.

$$1500+4500x<\frac{5-1}{5}\times 6000x$$

Subtract 1 from 5 to get 4.

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

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

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

Multiply 4 and 6000 to get 24000.

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

Divide 24000 by 5 to get 4800.

$$1500+4500x<4800x$$

Subtract 4800x from both sides.

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

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

$$1500-300x<0$$

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.

$$x>5$$