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Mathematics

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

2x – 5 ≤ 5x + 4 < 11, x ∈ R

Linear Inequations

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Answer

Given,

⇒ 2x – 5 ≤ 5x + 4 < 11

Solving L.H.S. of the inequation,

⇒ 2x – 5 ≤ 5x + 4

⇒ 5x + 4 ≥ 2x – 5

⇒ 5x - 2x ≥ -5 - 4

⇒ 3x ≥ -9

⇒ x ≥ −93-\dfrac{9}{3}

⇒ x ≥ -3 ………(1)

Solving R.H.S. of the inequation,

⇒ 5x + 4 < 11

⇒ 5x < 11 - 4

⇒ 5x < 7

⇒ x < 75\dfrac{7}{5}

⇒ x < 1.4 ……….(2)

From (1) and (2) we get,

-3 ≤ x < 1.4

Since, x ∈ R

Hence, solution set = {x : -3 ≤ x < 1.4, x ∈ R}.

Solution on the number line is :

2x – 5 ≤ 5x + 4 < 11, x ∈ R. Linear Inequations, RSA Mathematics Solutions ICSE Class 10.

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