Question

If the replacement set is the set of natural numbers, Find the set with maximum elements:

1) $x-5<0$

2) $x+1\le 7$

3) $3x-4>6$

4) $4x+1>17$

Answer 1

(1)

$x-5<0$

$x<5$

$x=\{1,2,3,4\}$

(2)

$x+1\le 7$

$x\le 7-1$

$x\le 6$

$x=\{1,2,3,4,5,6\}$

(3)

$3x-4>6$

$3x>6+4$

$3x>10$

$x>\frac{10}{3}$

$x=\{4,5,6,7,........\}$

(4)

$4x+1>17$

$4x>17-1$

$4x>16$

$x>\frac{16}{4}$

$x>4$

$x=\{5,6,7,........\}$

So, the set represented by equation (3) has maximum elements.