Question

Solve $12+1\frac{5}{6}x\le 5+3x$ when

$\left(i\right)xϵN$

$\left(ii\right)xϵR$

Draw the graph of the solution set in each case.

Answer 1

$12+1\frac{5}{6}x\le 5+3x$

$\Rightarrow 12+\frac{11}{6}x\le 5+3x$
$\Rightarrow 72+11x\le 30+18x$[multiplying both sides by 6]

$\Rightarrow 11x\le 18x-42$[adding - 72 to both sides]

$\Rightarrow -7x\le -42$[adding - 18x to both sides]

$\Rightarrow x\ge 6$[dividing both sides by -7]

(i) set = $\{xϵN:x\ge 6\}$

$=\{6,7,8,9,\dots \}$
The graph of this set is the number line, shown below.

The darkened circles indicate the natural numbers contained in the set. Three dots above the right part of the line show that the natural numbers are continued indefinitely.

(ii) set $=\{xϵR:x\ge 6\}=[6,\infty )$.

The graph of this set is shown below.

This graph consists of 6 all real numbers greater than 6.