Answer:
[tex]x[/tex] can be [tex]3[/tex], [tex]4[/tex], or [tex]5[/tex]
Step-by-step explanation:
Let's split the inequality and solve it piece by piece.
Case: [tex]3<=3x-4[/tex]
We add [tex]4[/tex] to both sides to get [tex]7<=3x[/tex].
We divide both sides by [tex]3[/tex] to get [tex]7/3<=x[/tex].
So, [tex]x>=7/3[/tex].
Case: [tex]3x-4<=2x+1[/tex]
We subtract 2x from both sides to get [tex]x-4<=1[/tex].
We add [tex]4[/tex] to both sides to get [tex]x<=5[/tex].
So, we want to find the integer solutions to [tex]7/3<=x<=5[/tex].
[tex]7/3= 2 1/3[/tex], so [tex]x[/tex] can be [tex]3[/tex], [tex]4[/tex], or [tex]5[/tex].
So, [tex]x[/tex] can be [tex]3[/tex], [tex]4[/tex], or [tex]5[/tex] and we're done!
