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Mathematics

Solve the following inequation and represent the solution set on the number line 2x - 5 ≤ 5x + 4 < 11, where x ∈ I.

Linear Inequations

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Answer

Given,

2x - 5 ≤ 5x + 4 < 11

Solving L.H.S. of the equation,

⇒ 2x - 5 ≤ 5x + 4

⇒ 5x - 2x ≥ -5 - 4

⇒ 3x ≥ -9

⇒ x ≥ -3 …….(i)

Solving R.H.S. of the equation,

⇒ 5x + 4 < 11

⇒ 5x < 11 - 4

⇒ 5x < 7

⇒ x < 75\dfrac{7}{5} …….(ii)

From (i) and (ii) we get,

-3 ≤ x < 75\dfrac{7}{5}

Since, x ∈ I

∴ Solution set = {-3, -2, -1, 0, 1}.

Solution on the number line is :

Solve the following inequation and represent the solution set on the number line 2x - 5 ≤ 5x + 4 < 11, where x ∈ I. Linear Inequations, Concise Mathematics Solutions ICSE Class 10.

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