Mathematics
Given x ∈ {real numbers}, find the range of values of x for which -5 ≤ 2x - 3 < x + 2 and represent it on a real number line.
Linear Inequations
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Answer
Given,
-5 ≤ 2x - 3 < x + 2
Solving L.H.S. of the equation,
⇒ -5 ≤ 2x - 3
⇒ 2x ≥ -5 + 3
⇒ 2x ≥ -2
Dividing both sides by 2 we get,
⇒ x ≥ -1 ……..(i)
Solving R.H.S. of the equation,
⇒ 2x - 3 < x + 2
⇒ 2x - x < 2 + 3
⇒ x < 5 ……..(ii)
From (i) and (ii) we get,
-1 ≤ x < 5.
∴ Solution set = {x : x ∈ R and -1 ≤ x < 5}.
Solution on the number line is :
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