1) 2х+3 <<u> x+3
x x-3
2x+3 - x+3 <0<br> x x-3
(2x+3)(x-3)-x(x+3) <0<br> x(x-3)
2x²+3x-6x-9-x²-3x <0<br> x(x-3)
x²-6x-9 <0<br> x(x-3)
x²-6x+9-18 <0<br> x(x-3)
(x-3)²-(3√2)² <0<br> x(x-3)
(x-3-3√2)(x-3+3√2) <0<br> x(x-3)
{x≠0
{x≠3
{x(x-3)(x-3-3√2)(x-3+3√2)<0<br>
x(x-3)(x-3-3√2)(x-3+3√2)<0<br>x(x-3)(x-7.24)(x+1.24)<0<br>
x=0 x=3 x=3+3√2 x=3-3√2
+ - + - +
--------- 3-3√2 -------- 0 ------- 3 -------- 3+3√2 -------------
\\\\\\\\\\\ \\\\\\\\\\\
x∈(3-3√2; 0)∨(3; 3+3√2)
2) x²+4x ≤ 2x
x+2 3
x(x+4) - 2x ≤ 0
x+2 3
3x(x+4)-2x(x+2) ≤0
3(x+2)
3x²+12x-2x²-4x ≤0
3(x+2)
x²+8x ≤0
3(x+2)
x(x+8) ≤ 0
3(x+2)
{3x(x+8)(x+2)≤0
{x≠2
3x(x+8)(x+2)≤0
x(x+8)(x+2)≤0
x=0 x=-8 x=-2
- + - +
-------- -8 ------ -2 ------- 0 ---------
\\\\\\\\\\ \\\\\\\\\\
x∈(-∞; -8]∨(-2; 0]