Question

What are the integer solutions to the inequality below? %20%5C%202x%2B1" id="TexFormula1" title="3\leq 3x-4\ \textless \ 2x+1" alt="3\leq 3x-4\ \textless \ 2x+1" align="absmiddle" class="latex-formula">

Answer 1

Given:

The compound inequality is:

$3\leq 3x-4$

To find:

The integer solutions for the given compound inequality.

Solution:

We have,

$3\leq 3x-4$

Case 1: $3\leq 3x-4$

$3+4\leq 3x$

$\dfrac{7}{3}\leq x$

$2.33...\leq x$             ...(i)

Case 2: $3x-4$

$3x-2x$

$x$                  ...(ii)

Using (i) and (ii), we get

$2.33...$

The integer values which satisfy this inequality are only 3 and 4.

Therefore, the integer solutions to the given inequality are 3 and 4.