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Mathematics

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

-3 < 2x - 1 < x + 4, x ∈ I

Linear Inequations

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Answer

Given,

⇒ -3 < 2x - 1 < x + 4

Solving L.H.S. of the inequation,

⇒ -3 < 2x – 1

⇒ 2x – 1 > -3

⇒ 2x > -3 + 1

⇒ 2x > -2

⇒ x > −22\dfrac{-2}{2}

⇒ x > -1 ….(1)

Solving R.H.S. of the inequation,

⇒ 2x - 1 < x + 4

⇒ 2x - x < 4 + 1

⇒ x < 5 …..(2)

From (1) and (2) we get,

⇒ -1 < x < 5

Since, x ∈ I.

Hence, solution set = {0, 1, 2, 3, 4}.

Solution on the number line is :

-3 < 2x - 1 < x + 4, x ∈ I. Linear Inequations, RSA Mathematics Solutions ICSE Class 10.

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