Question
Mathematics Question on Algebraic Solutions of Linear Inequalities in One Variable and their Graphical Representation
Solve the inequalities and represent the solution graphically on number line: 5(2x –7) – 3(2x+3) ≤ 0, 2x+19 ≤ 6x+47.
Answer
5(2x – 7) – 3(2x + 3) ≤ 0
⇒ 10x – 35 – 6x – 9 ≤ 0
⇒ 4x – 44 ≤ 0
⇒ 4x ≤ 44
⇒ x ≤ 11 ..… (1)
2x + 19 ≤ 6x + 47
⇒ 19 – 47 ≤ 6x – 2x
⇒ –28 ≤ 4x
⇒ –7 ≤ x ..… (2)
From (1) and (2), it can be concluded that the solution set for the given system of inequalities is [–7, 11].
The solution of the given system of inequalities can be represented on number line as
