Mathematics

Solve the inequation given below. Write the solution set and represent it on the number line:
5x - 11 ≤ 7x - 5 < 9, x ∈ R

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Solving L.H.S. of the inequation,

⇒ 5x - 11 ≤ 7x - 5

⇒ 7x - 5 ≥ 5x - 11

⇒ 7x - 5x ≥ -11 + 5

⇒ 2x ≥ -6

⇒ x ≥ $-\dfrac{6}{2}$

⇒ x ≥ -3 ……..(1)

Solving R.H.S. of the inequation,

⇒ 7x - 5 < 9

⇒ 7x < 9 + 5

⇒ 7x < 14

⇒ x < $\dfrac{14}{7}$

⇒ x < 2 ….(2)

From (1) and (2) we get,

-3 ≤ x < 2

Since, x ∈ R

Hence, solution set = {x : -3 ≤ x < 2, x ∈ R}.

Solution on the number line is :

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