Mathematics
If x ∈ Z, solve : 2 + 4x < 2x - 5 ≤ 3x. Also, represent its solution on the real number line.
Linear Inequations
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Answer
Given,
⇒ 2 + 4x < 2x - 5 ≤ 3x
Solving L.H.S. of the above inequation :
⇒ 2 + 4x < 2x - 5
⇒ 4x - 2x < - 5 - 2
⇒ 2x < -7
⇒ x <
⇒ x < -3.5 ……….(1)
Solving R.H.S. of the above inequation :
⇒ 2x - 5 ≤ 3x
⇒ 3x - 2x ≥ -5
⇒ x ≥ -5 ………….(2)
From (1) and (2), we get :
-5 ≤ x < -3.5; Since, x ∈ Z
Hence, x = {-5, -4}.
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