Solve x(1+8%)+x(1-10%)-2x/2x*100%

$$\frac { x ( 1 + 8 \% ) + x ( 1 - 10 \% ) - 2 x } { 2 x } \times 100 \%$$

Evaluate

$$-\frac{1}{100}=-0.01$$

Solution Steps

Divide 100 by 100 to get 1.

$$\frac{x\left(1+\frac{8}{100}\right)+x\left(1-\frac{10}{100}\right)-2x}{2x}\times 1$$

Reduce the fraction \frac{8}{100} to lowest terms by extracting and canceling out 4.

$$\frac{x\left(1+\frac{2}{25}\right)+x\left(1-\frac{10}{100}\right)-2x}{2x}\times 1$$

Convert 1 to fraction \frac{25}{25}.

$$\frac{x\left(\frac{25}{25}+\frac{2}{25}\right)+x\left(1-\frac{10}{100}\right)-2x}{2x}\times 1$$

Since \frac{25}{25} and \frac{2}{25} have the same denominator, add them by adding their numerators.

$$\frac{x\times \frac{25+2}{25}+x\left(1-\frac{10}{100}\right)-2x}{2x}\times 1$$

Add 25 and 2 to get 27.

$$\frac{x\times \frac{27}{25}+x\left(1-\frac{10}{100}\right)-2x}{2x}\times 1$$

Reduce the fraction \frac{10}{100} to lowest terms by extracting and canceling out 10.

$$\frac{x\times \frac{27}{25}+x\left(1-\frac{1}{10}\right)-2x}{2x}\times 1$$

Convert 1 to fraction \frac{10}{10}.

$$\frac{x\times \frac{27}{25}+x\left(\frac{10}{10}-\frac{1}{10}\right)-2x}{2x}\times 1$$

Since \frac{10}{10} and \frac{1}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x\times \frac{27}{25}+x\times \frac{10-1}{10}-2x}{2x}\times 1$$

Subtract 1 from 10 to get 9.

$$\frac{x\times \frac{27}{25}+x\times \frac{9}{10}-2x}{2x}\times 1$$

Combine x\times \frac{27}{25} and x\times \frac{9}{10} to get \frac{99}{50}x.

$$\frac{\frac{99}{50}x-2x}{2x}\times 1$$

Combine \frac{99}{50}x and -2x to get -\frac{1}{50}x.

$$\frac{-\frac{1}{50}x}{2x}\times 1$$

Cancel out x in both numerator and denominator.

$$\frac{-\frac{1}{50}}{2}\times 1$$

Express \frac{-\frac{1}{50}}{2} as a single fraction.

$$\frac{-1}{50\times 2}\times 1$$

Multiply 50 and 2 to get 100.

$$\frac{-1}{100}\times 1$$

Fraction \frac{-1}{100} can be rewritten as -\frac{1}{100} by extracting the negative sign.

$$-\frac{1}{100}$$

Factor

$$-\frac{1}{100} = -0.01$$