Question

Match the inequalities with their solution sets if x takes integer values only.

• A. $x=0,1,2,3,4$
• B. $x=4,5$
• C. $x=4,5,6,7$
• D. $x=-1,0,1,2,3,4$

Answer 1

Let's take the inequalities one by one to determine the solution set.

$x\le 4$ and $x>-1$

$\Rightarrow 4\le x>-1$

$\Rightarrow x=\{-1,0,1,2,3,4\}$

$x>3$ and $x\le 5$

$\Rightarrow 3<x\le 5$

$\Rightarrow x=\{4,5\}$

$x\ge -1$ and $x<5$

$\Rightarrow -1\le x<5$

$\Rightarrow x=\{-1,0,1,2,3,4\}$

$x\ge 4$ and $x\le 7$

$\Rightarrow 4\le x\le 7$

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