Solve each of the following inequalities expressing the answ

Solve each of the following inequalities, expressing the answers in terms of intervals. Show your work by following the steps given in Technique 1, 2 and 3 in Workbook for this topic. Use a proper Sign Analysis Method given on page 4.11 to page 4.13. 2(7x - 4) greaterthanorequalto 3x + 5 x^2 lessthanorequalto 3x + 4 x^3 greaterthanorequalto 25x x^3 + x

Solution

a)
2(7x-4) >= 3x+5
14x -8 >= 3x+5
11x >=13
x >= 13/11
Answer:
[13/11 ,inf)

b)
x^2 <= 3x+4
x^2- 3x - 4 < =0
(x-4)(x+1) <= 0
Answer:
[-1,4]

c)
x^3 >=25x
x^3-25x >=0
x (x^2-25) >= 0
x (x-5) (x+5) >=0
Answer:
[-5,0]U[5,inf)

d)
x^3 + x <=2x^2
x^3 - 2x^2 + x <= 0
x (x^2-2x+1)<=0
x (x-1)^2 < = 0
Answer:
(-inf,0]

i am allowed to answer only 4 parts at a time