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Mathematics

Find the greatest value of x ∈ Z, so that :
-1 ≤ 3 + 4x < 23

Linear Inequations

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Answer

Given,

-1 ≤ 3 + 4x < 23

Solving L.H.S. of the inequation,

⇒ -1 ≤ 3 + 4x

⇒ -1 - 3 ≤ 4x

⇒ -4 ≤ 4x

⇒ $\dfrac{-4}{4}$ ≤ x

⇒ -1 ≤ x

⇒ x ≥ -1 ….(1)

Solving R.H.S. of the inequation,

⇒ 3 + 4x < 23

⇒ 4x < 23 - 3

⇒ 4x < 20

⇒ x < $\dfrac{20}{4}$

⇒ x < 5 ….(2)

From (1) and (2) we get,

-1 ≤ x < 5

Since x ∈ Z,

x = {-1, 0, 1, 2, 3, 4}

Hence, greatest value of x is 4.

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