Question

Resolva em R, as inequações:
a) 3x - 4 ≤ x + 5

b) 2(x + 3)< - 2 (3x + 1)

d) x- 1 ≥ 3 + 2x
       2    2

Answer 1

A) 3x-4 ≤ x+5
    3x-x ≤ 5=4
2x ≤ 9
x ≤ 9/2

B) 2(x+3) < -2 (3x+1)
2x+6 < -2-6
8x<-8
x < -1

d) X-1/2 ≥ 3/2+2X
x-2x ≥ 3/2 + 1/2
-x ≥2 (-1)
x ≤ -2

Answer 2

a) 3x - 4 ≤ x + 5  ==> 3x - x <= 5 +4 => 2x <=9 ==> x<=9/2

b) 2(x + 3)< - 2 (3x + 1)  ==> 2x +6 < -6x -2 => 2x+6x < -2-6 ==>8x< -8 ==> x< -1

d) x- 1 ≥ 3 + 2x  mmc=2
        2   2

2x- 1  >= 3+4x 
2x-4x >= 3 + 1
      -2x>=4(-1)
2x<= - 4

x<= - 4/2

x<= - 2