Question

Given that $x$ is an integer, find the values of $x$ which satisfies both $2x+3>7$ and $x+4<10$.

• A. $3$
• B. $4$
• C. $4$ and $5$
• D. $3,4$ and $5$

Answer 1

The correct option is D $3,4$ and $5$

Consider the first inequality
$2x+3>7$
$2x>4$
$x>2$ ...(i)
Consider the second inequality
$x+4<10$
$x<6$ ...(ii)
From (i) and (ii), we have
$x\in (2,6)$ ...$(2$ and $6$ is not included since $2<x<6)$
It is given that $x$ is an integer.
Therefore integers lying between $(2,6)$ $(2$ and $6$ not included$)$ are $3,4,5$.
Hence, the integral values of $x$ satisfying the above given linear inequalities are $3,4,5$.