1.
a) 4-x≤2x-5
-x-2x≤ -5-4
-3x≤ -9
x≥3
б) 8-2x -2x-x< -1-8
-3x< -9
x>3
в) {x≥3
{x>3
x∈(3; +∞)
Ответ: (3; +∞).
2.
a) x² -x≥6
x² -x-6≥0
x²-x-6=0
D=1+24=25
x₁=(1-5)/2= -2
x₂=(1+5)/2=3
+ - +
--------- -2 -------------- 3 -----------
\\\\\\\\\\\\ \\\\\\\\\\\\
x∈(-∞; -2]U[3; +∞)
б) x+1≥1
x≥1-1
x≥0
в) {x∈(-∞; -2]U[3; +∞)
{x≥0
x∈[3; +∞)
Ответ: [3; +∞)
4.
x²+2x≥0
x(x+2)≥0
x=0 x= -2
+ - +
-------- -2 ----------- 0 -----------
\\\\\\\\\\\ \\\\\\\\\\\\\\
x∈(-∞; -2]U[0; +∞)
D(y)=(-∞; -2]U[0; +∞)