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Question
Solve the following inequalities and represent the solution graphically on number line:
3x – 7 > 2(x – 6), 6 – x > 11 – 2x
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Solution
3x – 7 > 2(x – 6)
⇒ 3x – 7 > 2x – 12
⇒ 3x – 2x > – 12 + 7
⇒ x > –5 …(1)
6 – x > 11 – 2x
⇒ –x + 2x > 11 – 6
⇒ x > 5 …(2)
From (1) and (2), it can be concluded that the solution set for the given system of inequalities is `(5, ∞)`. The solution of the given system of inequalities can be represented on number line as
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