Find the complete solution to the inequality : x^3 – 8 ≤ 7x – 14 (A) x ≤ – 3 or x ≥ 1 (B) – 3 ≤ x ≤ 1 (C) – 3 ≤ x ≤ 1 or x ≥ 2 (D) x ≤ – 3 or 1 ≤ x ≤ 2

2
by stswati14

• Brainly User
2015-05-13T09:50:06+05:30
X³ - 8 ≤  7x - 14
x³ - 7x  - 6 ≤ 0
let this equation = x³ - 7 x -6  = 0 then find the number of x whick makes it 0 then put x = 3  because if we put x = 3 we get 3³ - 7×3  - 6 = 0 rytee
then x = 3    x- 3 is a factor of this equation u already know because tumne isko  9th me pdha tha  theek h na now u get it
divide this equation by x- 3
x³ - 7x - 6 ÷ x+3
do it ur self
after solving it we get (x-1)(x-2)(x+3) are the zeros of this equation
on representing these numbers on number line u get 4  cases first
∞ < x ≤ -3 second  -3≤ x < 1 third 1 ≤ x <2  forth 2 ≤ x ∞
on checking it we will analyse  that x ≤ - 3 then we can say that than we can say that it implies negative than value of x lies for (- ∞ to -3]
second case [-3 to 1 ]  third  x ≥ 2 means x lies for [2 to ∞ ] fourth x ≤ -3 means x lies from [- 3 to - ∞)  we take only commen part in our answer
so commen part it (-∞ , -3] union [-3 , ∞)

2015-05-13T11:37:35+05:30
X³ - 8 ≤  7x - 14
x³ - 7x  - 6 ≤ 0
let this equation = x³ - 7 x -6  = 0 then find the number of x whick makes it 0 then put x = 3  because if we put x = 3 we get 3³ - 7×3  - 6 = 0 rytee
then x = 3    x- 3 is a factor of this equation u already know because tumne isko  9th me pdha tha  theek h na now u get it
divide this equation by x- 3
x³ - 7x - 6 ÷ x+3
do it ur self
after solving it we get (x-1)(x-2)(x+3) are the zeros of this equation
on representing these numbers on number line u get 4  cases first
∞ < x ≤ -3 second  -3≤ x < 1 third 1 ≤ x <2  forth 2 ≤ x ∞
on checking it we will analyse  that x ≤ - 3 then we can say that than we can say that it implies negative than value of x lies for (- ∞ to -3]
second case [-3 to 1 ]  third  x ≥ 2 means x lies for [2 to ∞ ] fourth x ≤ -3 means x lies from [- 3 to - ∞)  we take only commen part in our answer
so commen part it (-∞ , -3] union [-3 , ∞)