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
[tex] \frac{-2x}{-2} \ \textless \ \frac{2}{-2} [/tex]
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
[tex] \frac{-3x}{-3} \geq \frac{-3}{-3} [/tex]
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
[tex] \frac{-1.5x}{-1.5} \ \textgreater \ \frac{-1.3}{-1.5} [/tex]
x<0.866667
d)[tex] \frac{x}{2} + \frac{1}{4} \leq \frac{1}{2} [/tex]
[tex]\frac{x}{2}x + \frac{1}{4} \leq \frac{1}{2} [/tex]
[tex]\frac{x}{2}x + \frac{1}{4}- \frac{1}{4} \leq \frac{1}{2} - \frac{1}{4} [/tex]
[tex]\frac{x}{2}x \leq \frac{1}{4} [/tex]
[tex]2*( \frac{1}{2} x) \leq 2*( \frac{1}{4} )[/tex]
[tex]x \leq \frac{1}{2} [/tex]
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]
[tex] \frac{-x+4}{x+1} \leq 0[/tex]
[tex]\frac{-x+4}{x+1} =0[/tex]
−x+4=0
−x+4−4=0−4
−x=−4
[tex] \frac{-x}{-1} = \frac{-4}{-1} [/tex]
x=4
c)x−4x+3<0
−3x+3<0
−3x+3−3<0−3−3x<−3
[tex] \frac{-3x}{-3} \ \textless \ \frac{-3}{-3} [/tex]
x>1
