Question

Match the following inequalities with their solution sets.

• A. $x=\{4,5,6,7\}$
• B. $x=\{5,6,7\}$
• C. $x=\{4,5,6\}$
• D. $x=\{5,6\}$

Answer 1

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

a. $x>4$ and $x\le 7$
$\Rightarrow 4<x\le 7$
$\Rightarrow x=\{5,6,7\}$

b. $x>4$ and $x<7$
$\Rightarrow 4<x<7$
$\Rightarrow x=\{5,6\}$

c. $x\ge 4$ and $x<7$
$\Rightarrow 4\le x<7$
$\Rightarrow x=\{4,5,6\}$

d. $x\ge 4$ and $x\le 7$
$\Rightarrow 4\le x\le 7$
$\Rightarrow x=\{4,5,6,7\}$