Question

Given A = $x:11x-5>7x+3,xϵR$ and $B=x:18x-9\ge 15+12x,xϵR.$
Find the range of set $A\cap B$ and represent it on a number line.$\left[4Marks\right]$

Answer 1

We have:
$11x-5>7x+3$
$\Rightarrow 11x-5>7x+3$
$\Rightarrow 11x-7x>5+3$
$\Rightarrow 4x>8$
$\Rightarrow x>2$
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$\therefore A=\{x:x>2,xϵR\}$ ...(i)
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We also have
$18x-9\ge 15+12x$
$\Rightarrow 18x-9+9\ge 15+12x+9$
$\Rightarrow 18x-12x\ge 24$
$\Rightarrow 6x\ge 4$
$\Rightarrow x\ge 4$
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$\therefore B=\{x:x\ge 4,xϵR\}$ ...(ii)
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The range of set $A\cap B=\{x:x\ge 4,xϵR\}$
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The graph of $A\cap B$ is shown by thick portion of the number line


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