Question

Sa se rezolve inecuatiile

Answer 1

15x-5$\leq$0

15x$\leq$5 | 5

3x$\leq$1

x$\leq$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)$\leq$ 7x-14

10-5x$\leq$7x-14

-5x-7x$\leq$ -14-10

-12x$\leq$ -24

12x$\geq$24

x$\geq$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 $\leq$ 2(x+1) + 2  

{4-2x $\leq$ -5x+2

⇔

{x+3 $\leq$2x+2+2

{4-2x $\leq$ -5x+2

⇔

{x+3 $\leq$ 2x+4

{4-2x $\leq$ -5x+2

⇔

{ x-2x $\leq$ 4-3

{ -2x +5x$\leq$2-4

⇔

{ -x $\leq$ 1

{ 3x $\leq$ -2

⇔

{ x $\geq$ -1

{ x $\leq$ -2/3

-2/3 $\leq$ x $\geq$ -1 => x ∈ [-2/3; -1]