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Mathematics

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

1 ≥ 15 – 7x > 2x – 27, x ∈ N

Linear Inequations

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Answer

Given,

⇒ 1 ≥ 15 – 7x > 2x – 27

Solving L.H.S. of the inequation,

⇒ 1 ≥ 15 – 7x

⇒ 7x ≥ -1 + 15

⇒ 7x ≥ 14

⇒ x ≥ −147\dfrac{-14}{7}

⇒ x ≥ 2 ………(1)

Solving R.H.S. of the inequation,

⇒ 15 – 7x > 2x – 27

⇒ 2x – 27 < 15 – 7x

⇒ 2x + 7x < 15 + 27

⇒ 9x < 42

⇒ x < 429\dfrac{42}{9}

⇒ x < 4694\dfrac{6}{9} …….(2)

From (1) and (2) we get,

2 ≤ x < 4694\dfrac{6}{9}

Since, x ∈ N

Hence, solution set = {2, 3, 4}.

Solution on the number line is :

1 ≥ 15 – 7x > 2x – 27, x ∈ N. Linear Inequations, RSA Mathematics Solutions ICSE Class 10.

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