Question

Rezolvaţi, în mulţimea numerelor reale, ecuațiile:
a) 0,25x - 0,5 = 0,1 • (x + 1);
b) x - 1,2 • (x - 1) = 0,6x + 0,4;
urgent!!!!!!​

Answer 1

Răspuns:

a)x=4, b) x=1

Explicație pas cu pas:

a)0,25x-0,1x=0,5+0,1=> 0,15x=0,6=> x=0,6/0,15=> x=4

b)x-1,2x+1,2=0,6x+0,4=>-0,2x-0,6x=0,4-1,2=>-0,8x=-0,8=>x=0,8/0,8=1

Answer 2

$a)\hspace{6}0,25x-0,5=0,1\cdot(x+1)\iff\frac{25}{100}x-\frac{5}{10}=\frac{1}{10}\cdot(x+1)\iff\frac{x}{4}-\frac{1}{2}=\frac{x+1}{10}\iff\frac{x}{4}-\frac{2}{4}=\frac{x+1}{10}\iff\frac{x-2}{4}=\frac{x+1}{10}\implies(x-2)\cdot10=(x+1)\cdot4\implies10x-20=4x+4\implies10x-4x=4+20\iff6x=24\implies x=\frac{24}{6}=4\in\mathbb{R}$$b)\hspace{6}x-1,2\cdot(x-1)=0,6x+0,4\iff x-\frac{12\cdot(x-1)}{10}=\frac{6x}{10}+\frac{4}{10}\iff \frac{10x-12(x-1)}{10}=\frac{6x+4}{10}\iff\frac{5x-6(x-1)}{5}=\frac{3x+2}{5}\implies5x-6x+6=3x+2\implies-x+6=3x+2\implies-4x=-4/\cdot(-1)\implies4x=4\implies x=1\in\mathbb{R}$