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Mathematics

Solve the following inequation. Write down the solution set and represent it on the real number line.

-5(x - 9) ≥ 17 - 9x > x + 2, x ∈ R.

Linear Inequations

ICSE 2023

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Answer

Given, equation :

-5(x - 9) ≥ 17 - 9x > x + 2

Solving L.H.S. of the given equation :

⇒ -5(x - 9) ≥ 17 - 9x

⇒ -5x + 45 ≥ 17 - 9x

⇒ -5x + 9x ≥ 17 - 45

⇒ 4x ≥ -28

⇒ x ≥ −284-\dfrac{28}{4}

⇒ x ≥ -7 …………(1)

Solving L.H.S. of the given equation :

⇒ 17 - 9x > x + 2

⇒ x + 9x < 17 - 2

⇒ 10x < 15

⇒ x < 1510\dfrac{15}{10}

⇒ x < 32\dfrac{3}{2}

⇒ x < 1.5 ………….(2)

From equation (1) and (2), we get :

Solution set : {x : -7 ≤ x < 1.5}

Solution set on the number line :

Solve the following inequation. Write down the solution set and represent it on the real number line. ICSE 2023 Maths Solved Question Paper.

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