Given A = x:11x−5>7x+3,xϵR and B=x:18x−9≥15+12x,xϵR.
Find the range of set A∩B and represent it on a number line.
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Solution
We have: 11x - 5 > 7x + 3 ⇒11x−5>7x+3 ⇒11x−7x>5+3 ⇒4x>8 ⇒x>2 ∴A={x:x>2,xϵR} ...(i)
We also have 18x−9≥15+12x ⇒18x−9+9≥15+12x+9 ⇒18x−12x≥24 ⇒6x≥4 ⇒x≥4 ∴B={x:x≥4,xϵR} ...(ii)
The range of set A∩B={x:x≥4,xϵR}
The graph of A∩B is shown by thick portion of the number line