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Mathematics

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

-5(x - 9) ≥ 17 - 9x > x + 2, x ∈ R

Linear Inequations

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Answer

Given,

⇒ -5(x - 9) ≥ 17 - 9x > x + 2

Solving L.H.S. of the inequation,

⇒ -5(x - 9) ≥ 17 - 9x

⇒ -5x + 45 ≥ 17 - 9x

⇒ -5x + 9x ≥ 17 - 45

⇒ 4x ≥ 17 - 45

⇒ 4x ≥ -28

⇒ x ≥ −284-\dfrac{28}{4}

⇒ x ≥ -7 ………(1)

Solving R.H.S. of the inequation,

⇒ 17 - 9x > x + 2

⇒ x + 2 < 17 - 9x

⇒ x + 9x < 17 - 2

⇒ 10x < 15

⇒ x < 1510\dfrac{15}{10}

⇒ x < 32\dfrac{3}{2} …….(2)

From (1) and (2) we get,

⇒ -7 ≤ x < 32\dfrac{3}{2}

Since, x ∈ R

Hence, solution set = {x : -7 ≤ x < 32\dfrac{3}{2}, x ∈ R}.

Solution on the number line is :

-5(x - 9) ≥ 17 - 9x > x + 2, x ∈ R. Linear Inequations, RSA Mathematics Solutions ICSE Class 10.

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