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

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

Solve for x

$$x>119985$$

Solution Steps

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

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

Use the distributive property to multiply \frac{3}{4} by x-1.

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

Multiply \frac{3}{4} and -1 to get -\frac{3}{4}.

$$6000+\frac{3}{4}x-\frac{3}{4}<\frac{80}{100}x$$

Convert 6000 to fraction \frac{24000}{4}.

$$\frac{24000}{4}+\frac{3}{4}x-\frac{3}{4}<\frac{80}{100}x$$

Since \frac{24000}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{24000-3}{4}+\frac{3}{4}x<\frac{80}{100}x$$

Subtract 3 from 24000 to get 23997.

$$\frac{23997}{4}+\frac{3}{4}x<\frac{80}{100}x$$

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

$$\frac{23997}{4}+\frac{3}{4}x<\frac{4}{5}x$$

Subtract \frac{4}{5}x from both sides.

$$\frac{23997}{4}+\frac{3}{4}x-\frac{4}{5}x<0$$

Combine \frac{3}{4}x and -\frac{4}{5}x to get -\frac{1}{20}x.

$$\frac{23997}{4}-\frac{1}{20}x<0$$

Subtract \frac{23997}{4} from both sides. Anything subtracted from zero gives its negation.

$$-\frac{1}{20}x<-\frac{23997}{4}$$

Multiply both sides by -20, the reciprocal of -\frac{1}{20}. Since -\frac{1}{20} is negative, the inequality direction is changed.

$$x>-\frac{23997}{4}\left(-20\right)$$

Express -\frac{23997}{4}\left(-20\right) as a single fraction.

$$x>\frac{-23997\left(-20\right)}{4}$$

Multiply -23997 and -20 to get 479940.

$$x>\frac{479940}{4}$$

Divide 479940 by 4 to get 119985.

$$x>119985$$