How do you solve x-5=-3/2x+5/2?

May 11, 2018

$x = 3$

Explanation:

$\text{to eliminate fractions multiply all terms on both sides of}$
$\text{the equation by 2}$

$\Rightarrow 2 x - 10 = \cancel{2} \times - \frac{3 x}{\cancel{2}} + \cancel{2} \times \frac{5}{\cancel{2}}$

$\Rightarrow 2 x - 10 = - 3 x + 5 \leftarrow \textcolor{b l u e}{\text{no fractions}}$

$\text{add "3x" to both sides}$

$2 x + 3 x - 10 = \cancel{- 3 x} \cancel{+ 3 x} + 5$

$\Rightarrow 5 x - 10 = 5$

$\text{add 10 to both sides}$

$5 x \cancel{- 10} \cancel{+ 10} = 5 + 10$

$\Rightarrow 5 x = 15$

$\text{divide both sides by 5}$

$\frac{\cancel{5} x}{\cancel{5}} = \frac{15}{5}$

$\Rightarrow x = 3 \text{ is the solution}$

May 11, 2018

$x = 3$

Explanation:

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

$\text{multiply" L.H.S and R.H.S. by} 2$

$\therefore 2 x - 10 = - {\cancel{6}}^{3} / {\cancel{2}}^{1} x + {\cancel{10}}^{5} / {\cancel{2}}^{1}$

$\therefore 2 x - 10 = - 3 x + 5$

$\therefore 2 x + 3 x = 5 + 10$

$\therefore 5 x = 15$

$\therefore x = {\cancel{15}}^{3} / {\cancel{5}}^{1}$

$\therefore x = 3$

~~~~~~~~~~~~

$\text{check:-}$

$\text{substitute } x = 3$

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

$\therefore - 2 = - \frac{9}{2} + \frac{5}{2}$

$\therefore - 2 = - {\cancel{4}}^{2} / {\cancel{2}}^{1}$

$\therefore - 2 = - 2$