Question

2. Calculați x din proporţiile:

Answer 1

$\displaystyle a)~\frac{x-1}{1+\cfrac{1}{2} }=\frac{\cfrac{7}{3}-1}{3-\cfrac{3}{2}} \Rightarrow\frac{x-1}{\cfrac{2+1}{2} }=\frac{\cfrac{7-3}{3} }{\cfrac{6-3}{2}} \Rightarrow \frac{x-1}{\cfrac{3}{2} } =\frac{\cfrac{4}{3} }{\cfrac{3}{2} }\Rightarrow (x-1) \cdot \frac{2}{3} =\frac{4}{3}\cdot\frac{2}{3}\Rightarrow\\\\\Rightarrow\frac{2x-2}{3} =\frac{8}{9}\Rightarrow (2x-2)\cdot 9=8\cdot3\Rightarrow18x-18=24\Rightarrow 18x=24+18\Rightarrow\\\\\Rightarrow18x=42\Rightarrow x=\frac{42}{18}\Rightarrow x=\frac{7}{3}$

$\displaystyle b)~\frac{2x+1}{4x+3} =\frac{1}{3} \Rightarrow (2x+1) \cdot 3=1 \cdot (4x+3) \Rightarrow 6x+3=4x+3 \Rightarrow \\\\ \Rightarrow 6x-4x=3-3 \Rightarrow 2x=0 \Rightarrow x=\frac{0}{2} \Rightarrow x=0$