Solve 80%xdivx*100%geq20%

$$80 \% x \div x \times 100 \% \geq 20 \%$$

Evaluate (complex solution)

Solution Steps

Divide 100 by 100 to get 1.

$$\frac{\frac{80}{100}x}{x}\times 1\geq \frac{20}{100}$$

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

$$\frac{\frac{4}{5}x}{x}\times 1\geq \frac{20}{100}$$

Cancel out x in both numerator and denominator.

$$\frac{4}{5}\times 1\geq \frac{20}{100}$$

Multiply \frac{4}{5} and 1 to get \frac{4}{5}.

$$\frac{4}{5}\geq \frac{20}{100}$$

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

$$\frac{4}{5}\geq \frac{1}{5}$$

Compare \frac{4}{5} and \frac{1}{5}.

$$\text{true}$$

Solve for x

$$x\neq 0$$

Solution Steps

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

$$\frac{\frac{4}{5}x}{x}\times \frac{100}{100}\geq \frac{20}{100}$$

Divide 100 by 100 to get 1.

$$\frac{\frac{4}{5}x}{x}\times 1\geq \frac{20}{100}$$

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

$$\frac{\frac{4}{5}x}{x}\times 1\geq \frac{1}{5}$$

Divide both sides by 1. Since 1 is positive, the inequality direction remains the same.

$$\frac{\frac{4}{5}x}{x}\geq \frac{\frac{1}{5}}{1}$$

Express \frac{\frac{1}{5}}{1} as a single fraction.

$$\frac{\frac{4}{5}x}{x}\geq \frac{1}{5\times 1}$$

Cancel out 1 in both numerator and denominator.

$$\frac{\frac{4}{5}x}{x}\geq \frac{1}{5}$$

The value of the expression \frac{4}{5}xx^{-1} is always positive. Inequality holds for x\in \mathrm{R}.

$$x\in \mathrm{R}$$