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Mathematics

Solve the inequation given below. Write the solution set and represent it on the number line:

2 + 4x < 2x - 5 < 3x, x ∈ I

Linear Inequations

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Answer

Given,

⇒ 2 + 4x < 2x - 5 < 3x

Solving L.H.S. of the inequation,

⇒ 2 + 4x < 2x - 5

⇒ 4x - 2x < -5 - 2

⇒ 2x < -7

⇒ x < −72-\dfrac{7}{2}

⇒ x < -3.5 ……….(1)

Solving R.H.S. of the inequation,

⇒ 2x - 5 < 3x

⇒ 3x - 2x > -5

⇒ x > -5 ………(2)

From (1) and (2) we get,

-5 < x < -3.5

Since, x ∈ I.

Hence, solution set = {-4}.

Solution on the number line is :

2 + 4x < 2x - 5 < 3x, x ∈ I. Linear Inequations, RSA Mathematics Solutions ICSE Class 10.

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