Question

Given that $x$ is an integer, find the values of $x$ which would 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 $2,3$

Consider the first inequality
$2+x<6$
$x<4$ ...$\left(i\right)$
Consider the second inequality
$2-3x<-1$
$3<3x$
$x>1$ ...$\left(ii\right)$
However, it is given that $x$ is an integer.
Therefore, the only integers in the between $1$ and $4$ ($1$ and $4$ not included because $1<x<4$) are $\{2,3\}$.
Hence, values of $x$ satisfying the simultaneous linear inequalities are $2,3$.