Question

Va rog ajutati-ma la urmatoarele exercitii:
1. Rezolva inecuatiile;
a) 2x +1 mai mic decat 3 + 4x
b) 2(1 - x) +1 mai mare sau egal decat x
c) 0,5x + 1,3 mai mare decat 2x
d) x pe 2 + 1 pe 4 mai mic sau egal decat 1 pe 2
2. Rezolva inecuatiile:
a) (3-x) (x+2) mai mare sau egal decat 0
b) 4-x pe 1+x mai mic sau egal decat 0
c) x la patrat - 4x +3 mai mic decat 0
Va rog sa ma ajutati cat mai repede

Answer 1

1.a)2x+1<3+4x2x+1<4x+3
2x+1−4x<4x+3−4x−2x+1<3
−2x+1−1<3−1−2x<2
$\frac{-2x}{-2} \ \textless \ \frac{2}{-2}$
x>−1
b)2(1−x)+1≥x
−2x+3≥x
−2x+3−x≥x−x−3x+3≥0
−3x+3−3≥0−3−3x≥−3
$\frac{-3x}{-3} \geq \frac{-3}{-3}$
x≤1
c)0.5x+1.3>2x
0.5x+1.3−2x>2x−2x−1.5x+1.3>0
−1.5x+1.3−1.3>0−1.3−1.5x>−1.3
$\frac{-1.5x}{-1.5} \ \textgreater \ \frac{-1.3}{-1.5}$
x<0.866667
d)$\frac{x}{2} + \frac{1}{4} \leq \frac{1}{2}$
$\frac{x}{2}x + \frac{1}{4} \leq \frac{1}{2}$
$\frac{x}{2}x + \frac{1}{4}- \frac{1}{4} \leq \frac{1}{2} - \frac{1}{4}$
$\frac{x}{2}x \leq \frac{1}{4}$
$2*( \frac{1}{2} x) \leq 2*( \frac{1}{4} )$
$x \leq \frac{1}{2}$
2.a)(3−x)(x+2)≥0−x2+x+6≥0
−x2+x+6=0(−x−2)(x−3)=0
−x−2=0 or x−3=0
x=−2 or x=3
b)[tex] \frac{4-x}{1+x} \leq 0 [/tex]
$\frac{-x+4}{x+1} \leq 0$
$\frac{-x+4}{x+1} =0$
−x+4=0
−x+4−4=0−4
−x=−4
$\frac{-x}{-1} = \frac{-4}{-1}$
x=4
c)x−4x+3<0
−3x+3<0
−3x+3−3<0−3−3x<−3
$\frac{-3x}{-3} \ \textless \ \frac{-3}{-3}$
x>1