Given:
The compound inequality is:
[tex]3\leq 3x-4<2x+1[/tex]
To find:
The integer solutions for the given compound inequality.
Solution:
We have,
[tex]3\leq 3x-4<2x+1[/tex]
Case 1: [tex]3\leq 3x-4[/tex]
[tex]3+4\leq 3x[/tex]
[tex]\dfrac{7}{3}\leq x[/tex]
[tex]2.33...\leq x[/tex] ...(i)
Case 2: [tex]3x-4<2x+1[/tex]
[tex]3x-2x<1+4[/tex]
[tex]x<5[/tex] ...(ii)
Using (i) and (ii), we get
[tex]2.33...<x<5[/tex]
The integer values which satisfy this inequality are only 3 and 4.
Therefore, the integer solutions to the given inequality are 3 and 4.
