Question

Sa se determine x din egalitatile :
a.$\frac{x+1}{5} = \frac{4}{2}$
b. $\frac{3}{5} = \frac{7x-2}{20}$
c. $\frac{5x-2}{2x+3} = \frac{8}{7}$

Answer 1

$\displaystyle a). \frac{x+1}{5} = \frac{4}{2} \Rightarrow 2(x+1)=5 \cdot 4\Rightarrow 2x+2=20 \Rightarrow 2x=20-2 \Leftrightarrow \\ \\ \Leftrightarrow 2x=18 \Rightarrow x= \frac{18}{2} \Rightarrow x=9 \\ \\ b). \frac{3}{5} = \frac{7x-2}{20} \Rightarrow 3 \cdot 20=5(7x-2) \Rightarrow 60=35x-10 \Leftrightarrow \\ \\ \Leftrightarrow -35x=-10-60 \Rightarrow -35x=-70 \Rightarrow x= \frac{-70}{-35} \Rightarrow x=2$

$\displaystyle c). \frac{5x-2}{2x+3} = \frac{8}{7} \Rightarrow 7(5x-2)=8(2x+3) \Rightarrow 35x-14=16x+24 \Leftrightarrow \\ \\ \Leftrightarrow 35x-16x=24+14 \Rightarrow 19x=38 \Rightarrow x= \frac{38}{19} \Rightarrow x=2$