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Mathematics

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

Linear Inequations

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Answer

Given,

7 ≥ -2x + 1 > -7

Solving L.H.S. of the inequation,

⇒ 7 ≥ -2x + 1

⇒ 7 - 1 ≥ -2x

⇒ 6 ≥ -2x

⇒ 2x ≥ -6

⇒ x ≥ −62\dfrac{-6}{2}

⇒ x ≥ -3 ….(1)

Solving R.H.S. of the inequation,

⇒ -2x + 1 > -7

⇒ -2x > -7 - 1

⇒ -2x > -8

⇒ 2x < 8

⇒ x < 82\dfrac{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

Hence, sum of greatest and smallest values of x = 0.

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