Solve 5/2x-40%-2x=5x+0.5

$$\frac { 5 } { 2 } x - 40 \% - 2 x = 5 x + 0.5$$

Solve for x

$$x=-0.2$$

Steps for Solving Linear Equation

Reduce the fraction \frac{40}{100} to lowest terms by extracting and canceling out 20.

$$\frac{5}{2}x-\frac{2}{5}-2x=5x+0.5$$

Combine \frac{5}{2}x and -2x to get \frac{1}{2}x.

$$\frac{1}{2}x-\frac{2}{5}=5x+0.5$$

Subtract 5x from both sides.

$$\frac{1}{2}x-\frac{2}{5}-5x=0.5$$

Combine \frac{1}{2}x and -5x to get -\frac{9}{2}x.

$$-\frac{9}{2}x-\frac{2}{5}=0.5$$

Add \frac{2}{5} to both sides.

$$-\frac{9}{2}x=0.5+\frac{2}{5}$$

Convert decimal number 0.5 to fraction \frac{5}{10}. Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$-\frac{9}{2}x=\frac{1}{2}+\frac{2}{5}$$

Least common multiple of 2 and 5 is 10. Convert \frac{1}{2} and \frac{2}{5} to fractions with denominator 10.

$$-\frac{9}{2}x=\frac{5}{10}+\frac{4}{10}$$

Since \frac{5}{10} and \frac{4}{10} have the same denominator, add them by adding their numerators.

$$-\frac{9}{2}x=\frac{5+4}{10}$$

Add 5 and 4 to get 9.

$$-\frac{9}{2}x=\frac{9}{10}$$

Multiply both sides by -\frac{2}{9}, the reciprocal of -\frac{9}{2}.

$$x=\frac{9}{10}\left(-\frac{2}{9}\right)$$

Multiply \frac{9}{10} times -\frac{2}{9} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{9\left(-2\right)}{10\times 9}$$

Cancel out 9 in both numerator and denominator.

$$x=\frac{-2}{10}$$

Reduce the fraction \frac{-2}{10} to lowest terms by extracting and canceling out 2.

$$x=-\frac{1}{5}$$