Question

Given that x is an integer, find the values of x which satisfy the simultaneous linear inequalities $2+x<6$ and $2-3x<-1$.

• A. $2,3$
• B. $1,2,3$
• C. $2,3,4$
• D. $1,2,3,4$

Answer 1

The correct option is A $2,3$

$2+x<6$

Add $-2$ on both sides, we get

$2+x-2<6-2$

$\Rightarrow x<4$

$2-3x<-1$

Add $-2$ on both sides, we get

$2-3x-2<-1-2$

$\Rightarrow -3x<-3$

$-3x÷(-3)>-3÷(-3)$

$\Rightarrow x>1$

Then, $1<x<4$ is $2,3$.