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What are the integer solutions to the inequality below? 3 ≤ 3 x − 4 ≤ 2 x + 1

Sagot :

danielgeyfman

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!

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