Solve the following inequation and graph the solution set on the number line: 2x−3<x+2≤3x+5,xϵR
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Solution
Given:2x−3<x+2≤3x+5,xϵR
First, we take 2x - 3 < x + 2 ⇒2x−x<2+3
[Transposing the terms] ⇒x<5 ...(i)
Now, x+2≤3x+5 ⇒2−5≤3x−x ⇒−3≤2x ⇒−1.5≤x ...(ii)
From equations (i) and (ii), we get −1.5≤x<5 ∴ Solution set is {x:−1.5≤x<5,xϵR}
Graph of the solution set is as follows: