Solve 5%x+3%(140-x)<5.8

$$5 \% x+3 \% (140-x) < 5.8$$

Solve for x

$$x<80$$

Solution Steps

Reduce the fraction \frac{5}{100} to lowest terms by extracting and canceling out 5.

$$\frac{1}{20}x+\frac{3}{100}\left(140-x\right)<5.8$$

Use the distributive property to multiply \frac{3}{100} by 140-x.

$$\frac{1}{20}x+\frac{3}{100}\times 140+\frac{3}{100}\left(-1\right)x<5.8$$

Express \frac{3}{100}\times 140 as a single fraction.

$$\frac{1}{20}x+\frac{3\times 140}{100}+\frac{3}{100}\left(-1\right)x<5.8$$

Multiply 3 and 140 to get 420.

$$\frac{1}{20}x+\frac{420}{100}+\frac{3}{100}\left(-1\right)x<5.8$$

Reduce the fraction \frac{420}{100} to lowest terms by extracting and canceling out 20.

$$\frac{1}{20}x+\frac{21}{5}+\frac{3}{100}\left(-1\right)x<5.8$$

Multiply \frac{3}{100} and -1 to get -\frac{3}{100}.

$$\frac{1}{20}x+\frac{21}{5}-\frac{3}{100}x<5.8$$

Combine \frac{1}{20}x and -\frac{3}{100}x to get \frac{1}{50}x.

$$\frac{1}{50}x+\frac{21}{5}<5.8$$

Subtract \frac{21}{5} from both sides.

$$\frac{1}{50}x<5.8-\frac{21}{5}$$

Convert decimal number 5.8 to fraction \frac{58}{10}. Reduce the fraction \frac{58}{10} to lowest terms by extracting and canceling out 2.

$$\frac{1}{50}x<\frac{29}{5}-\frac{21}{5}$$

Since \frac{29}{5} and \frac{21}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{50}x<\frac{29-21}{5}$$

Subtract 21 from 29 to get 8.

$$\frac{1}{50}x<\frac{8}{5}$$

Multiply both sides by 50, the reciprocal of \frac{1}{50}. Since \frac{1}{50} is positive, the inequality direction remains the same.

$$x<\frac{8}{5}\times 50$$

Express \frac{8}{5}\times 50 as a single fraction.

$$x<\frac{8\times 50}{5}$$

Multiply 8 and 50 to get 400.

$$x<\frac{400}{5}$$

Divide 400 by 5 to get 80.

$$x<80$$