I need help solving the equation below!!! What are the steps to solving it?
$\displaystyle \frac{2x}{5} - \frac{2x - 1}{2} = \frac{x}{5}$
Most people hate fractions, so let's get rid of these first. We need to find a common denominator, and I would choose 2 * 5 = 10. So I'm going to multiply both sides of the equation by 10:
$\displaystyle 10 \cdot \left ( \frac{2x}{5} - \frac{2x - 1}{2} \right ) = 10 \cdot \left ( \frac{x}{5} \right )$
$\displaystyle 2 \cdot (2x) - 5 \cdot (2x - 1) = 2 \cdot (x)$
$\displaystyle 4x - 10x + 5 = 2x$
$\displaystyle -6x + 5 = 2x$
$\displaystyle -2x - 6x + 5 = -2x + 2x$
$\displaystyle -8x + 5 = 0$
$\displaystyle -8x + 5 - 5 = 0 - 5$
$\displaystyle -8x = -5$
$\displaystyle \frac{-8x}{-8} = \frac{-5}{-8}$
$\displaystyle x = \frac{5}{8}$
-Dan