Question

If two algebraic inequalities for the same unknown integer $x$ are $x+2>9\&x-3<7$, then what are the possible values of $x$.

• A. $7,8,9\&10$
• B. $8\&9$
• C. $9{\&}^{}10$

Answer 1

The correct option is B $8\&9$

Given first algebraic inequality : $x+2>9$
Subtract $2$ from both sides of the inequality
$\Rightarrow x+2-2>9-2\Rightarrow x>7$

Given second algebraic inequality : $x-3<7$
Add $3$ on both sides of the inequality
$x-3+3<7+3\Rightarrow x<10$

$\Rightarrow 7<x<10$
here integeral values of $x$ are $8\&9$.