Question

If 7 ≥ −2x + 1 > −7; find the sum of greatest and smallest values of x ∈ I.

Answer 1

Given,

7 ≥ −2x + 1 > −7

Solving L.H.S. of the inequation,

⇒ 7 ≥ −2x + 1

⇒ 7 − 1 ≥ −2x

⇒ 6 ≥ −2x

⇒ 2x ≥ −6

⇒ x ≥ `(−6)/2`

⇒ x ≥ −3 ....(1)

Solving R.H.S. of the inequation,

⇒ −2x + 1 > −7

⇒ −2x > −7 − 1

⇒ −2x > −8

⇒ 2x < 8

⇒ x < `8/2`

⇒ x < 4 ....(2)

From (1) and (2) we get,

−3 ≤ x < 4

Since x ∈ I,

x = {−3, −2, −1, 0, 1, 2, 3}

Greatest value of x is 3 and smallest value of x is −3

The sum of greatest and smallest values of x = −3 + 3 = 0

∴ sum of greatest and smallest values of x = 0.