Question
Mathematics Question on Algebraic Solutions of Linear Inequalities in One Variable and their Graphical Representation
Solve the following inequalities and represent the solution graphically on number line: 3x –7 > 2(x-6), 6-x > 11-2x.
Answer
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