Question

MIC
E3
Să se determine numerele reale care
verifică inegalitățile:
a) |3x - 2| = 0; b) |4-6x| <sau = 0;
c) |x |< 3;
d) |3x - 4|-5 < sau=0;
e)| y -2 |> 0;
f) |a +5| > 0;
g)| x^5 - 1 |+| x ^6+9| > 0.​

Answer 1

$\it a)\ \ |3x-2|=0 \Rightarrow 3x-2=0 \Rightarrow 3x=2 \Rightarrow x=\dfrac{2}{3}\\ \\ b)\ |4-6x|\leq0 \Rightarrow 4-6x=0 \Rightarrow 4=6x \Rightarrow 6x=4 \Rightarrow x=\dfrac{\ 4^{(2}}{6} \Rightarrow x=\dfrac{2}{3}\\ \\ \\ c)\ \ |x|<3 \Rightarrow x\in\varnothing,\ modulul\ nu\ este\ niciodat\breve a\ negativ\\ \\ d)|3x-4|-5\leq0 \Rightarrow |3x-4|\leq5 \Rightarrow -5\leq3x-4\leq5|_{+4} \Rightarrow -1\leq3x\leq9|_{:3} \Rightarrow \\ \\ -\dfrac{1}{3}\leq x\leq3 \Rightarrow x\in\Big[-\dfrac{1}{3},\ 3\Big]$