What is the integer solution of the given linear inequation?
2 + 4x < 2x - 5 ≤ 3x, x ∈ Z

[2 marks]

{-6, -5, -4}

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{-5, -4}

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{-6, -5}

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{-3, -4}

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Solution

The correct option is B {-5, -4}
Given,

2 + 4x < 2x - 5 ≤ 3x

Let us separate the inequation into two inequalities.

2 + 4x < 2x - 5 and 2x - 5 ≤ 3x

Rule: If a term of an inequation is transferred from one side to the other side of the inequation, the sign of the term gets changed. Let us apply this rule to the above inequalities.

2x < -7 and -5 ≤ x

x < -3.5 and -5 ≤ x

-5 ≤ x < -3.5

Since x ∈ Z, the solution set is {-5, -4}.

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