Question

1. Rezolvati in multimea Q ecuatiile:
a) x + 3/4 = 7/8;
b) x - 1/2 * 5/4 = 1/12;
2. Rezolvati in multimea numerelor rationale ecuatiile:
a) 2x + 0,3 = 0,25;
b) 3x + 1/2 = 0,4;

Answer 1

$\displaystyle 1a).x+ \frac{3}{4} = \frac{7}{8} \\ \\ 8x+6=7 \\ \\ 8x=7-6 \\ \\ 8x=1 \Rightarrow \boxed{x= \frac{1}{8} } \\ \\ b).x- \frac{1}{2} \cdot \frac{5}{4} = \frac{1}{12} \\ \\ x- \frac{5}{8} = \frac{1}{12} \\ \\ 24x-15=2 \\ \\ 24x=2+15 \\ \\ 24x=17 \Rightarrow \boxed{ x= \frac{17}{24} }\\ \\ 2a).2x+0,3=0,25\\ \\ 2x+ \frac{3}{10} = \frac{1}{4} \\ \\ 80x+12=10 \\ \\ 80x=10-12 \\ \\ 80x=-2 \Rightarrow x=- \frac{2}{80} \Rightarrow \boxed{x=- \frac{1}{40} }$
$\displaystyle b).3x+ \frac{1}{2} =0,4 \\ \\ 3x+ \frac{1}{2} = \frac{2}{5} \\ \\ 30x+5=4 \\ \\ 30x=4-5 \\ \\ 30x=-1 \Rightarrow \boxed{x=- \frac{1}{30} }$