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Mathematics

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

2 ≤ 2x - 3 ≤ 5, x ∈ R

Linear Inequations

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Answer

Given,

⇒ 2 ≤ 2x - 3 ≤ 5

Solving L.H.S. of the inequation,

⇒ 2 ≤ 2x – 3

⇒ 2x - 3 ≥ 2

⇒ 2x ≥ 2 + 3

⇒ 2x ≥ 5

⇒ x ≥ 52\dfrac{5}{2}

⇒ x ≥ 2122\dfrac{1}{2} ………(1)

Solving R.H.S. of the inequation,

⇒ 2x - 3 ≤ 5

⇒ 2x ≤ 5 + 3

⇒ 2x ≤ 8

⇒ x ≤ 82\dfrac{8}{2}

⇒ x ≤ 4 …………(2)

From (1) and (2) we get,

2122\dfrac{1}{2} ≤ x ≤ 4

Since, x ∈ R

Hence, solution set = {x : 2122\dfrac{1}{2} ≤ x ≤ 4, x ∈ R}.

Solution on the number line is :

2 ≤ 2x - 3 ≤ 5, x ∈ R. Linear Inequations, RSA Mathematics Solutions ICSE Class 10.

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