Question

What are the integer solutions to the inequality below? 4x+1<5x≤3(x+2)

Answer 1

Given:

The inequality is:

$4x+1$

To find:

The integer solutions to the given inequality.

Solution:

We have,

$4x+1$

This compound inequality can be written as two separate inequalities $4x+1$ and $5x\leq 3(x+2)$.

Now,

$1$

$1$                 ...(i)

And,

$5x\leq 3(x+2)$

$5x\leq 3(x)+3(2)$

$5x-3x\leq 6$

$2x\leq 6$

Divide both sides by 2.

$x\leq \dfrac{6}{2}$

$x\leq 3$               ...(ii)

From (i) and (ii), we get

$1$

Here, 1 is excluded and 3 is included in the solution set. There two integer values 2 and 3 in $1$.

Therefore, the integer solution for the given inequality are 2 and 3.