15x-5[tex]\leq \\[/tex]0
15x[tex]\leq[/tex]5 | 5
3x[tex]\leq[/tex]1
x[tex]\leq[/tex]1/3 => x ∈ (-∞; 1/3]
5(x-3)-(x+1) > (x-2)*2 + 10
5x-15-x-1 > 2x-4+10
4x-16 > 2x + 6
4x-2x > 6+16
2x > 22
x > 11 => x ∈ (11; + ∞)
5(2-x)[tex]\leq[/tex] 7x-14
10-5x[tex]\leq[/tex]7x-14
-5x-7x[tex]\leq[/tex] -14-10
-12x[tex]\leq[/tex] -24
12x[tex]\geq[/tex]24
x[tex]\geq[/tex]2 => x∈[2; +∞)
(2x-1)/3 + 2 < (x-5)/6
2(2x-1+6) < x-5
4x-2+12 < x-5
4x+10 < x-5
4x-x < -5-10
3x < -15
x < -5 => x∈(-∞; -5)
(1-3x)/4 +1/2 > x-1
(1-3x+2)/4 > x-1
3-3x > 4x-4
-3x-4x > -4-3
-7x > -7
x < 1 => x∈ (-∞; 1)
(x+1)/(x+2) > 0
x+1 > 0
x > -1 => x∈(-1; +∞)
(3x-2)/(5-3x) > 1
3x-2 > 5-3x
3x+3x > 5+2
6x > 7
x > 7/6 => x∈( 7/6;+∞)
3x/(x-1) < -1
3x < 1-x
3x+x < 1
4x < 1
x< 1/4 => x∈(-∞; 1/4)
{x+3 [tex]\leq[/tex] 2(x+1) + 2
{4-2x [tex]\leq[/tex] -5x+2
⇔
{x+3 [tex]\leq[/tex]2x+2+2
{4-2x [tex]\leq[/tex] -5x+2
⇔
{x+3 [tex]\leq[/tex] 2x+4
{4-2x [tex]\leq[/tex] -5x+2
⇔
{ x-2x [tex]\leq[/tex] 4-3
{ -2x +5x[tex]\leq[/tex]2-4
⇔
{ -x [tex]\leq[/tex] 1
{ 3x [tex]\leq[/tex] -2
⇔
{ x [tex]\geq[/tex] -1
{ x [tex]\leq[/tex] -2/3
-2/3 [tex]\leq[/tex] x [tex]\geq[/tex] -1 => x ∈ [-2/3; -1]
