Question e1200

Jun 18, 2017

$x = 0$

Explanation:

$\text{distributing the brackets gives}$

$\frac{1}{2} x \cancel{- \frac{3}{2}} \cancel{+ \frac{3}{2}} - x = 5 x$

$\Rightarrow \frac{1}{2} x - x - 5 x = 0$

$\Rightarrow - \frac{11}{2} x = 0 \Rightarrow x = 0$

$\textcolor{b l u e}{\text{As a check}}$

$\text{left side } = \frac{1}{2} \left(- 3\right) + \frac{3}{2} = 0$

$\text{right side } = 5 \times 0 = 0$

$\Rightarrow x = 0 \text{ is the solution}$

Jun 18, 2017

color(green)(x=0

Explanation:

$\frac{1}{2} \left(x - 3\right) + \left(\frac{3}{2}\right) - x = 5 x$

$\therefore 0.5 x - 1.5 + 1.5 - x = 5 x$

$\therefore 0.5 x - x - 5 x = 1.5 - 1.5$

$\therefore 0.5 x - 6 x = 0$

$\therefore - 5.5 x = 0$

$\therefore x = \frac{0}{-} 5.5$

:.color(green)(x=0

Substitute $x = 0$

$\therefore \frac{1}{2} \left(\left(\textcolor{g r e e n}{0}\right) - 3\right) + \left(\frac{3}{2}\right) - \left(\textcolor{g r e e n}{0}\right) = 5 \left(0\right)$

$\therefore \left(0.5 \times 0\right) - 1.5 + 1.5 - 0 = 0$

$\therefore 0 - 1.5 + 1.5 - 0 = 0$

:.color(green)(0=0#