Respuesta :

We have been given two inequalities [tex]2x+9<0[/tex] and [tex]x>-12[/tex]. We are asked to find the integers that satisfy both inequalities.

Let us solve for our 1st inequality.

[tex]2x+9-9<0-9[/tex]

[tex]2x<-9[/tex]

[tex]\frac{2x}{2}<-\frac{9}{2}[/tex]

[tex]x<-4.5[/tex]

Upon combining our both inequalities, we will get:

[tex]-12<x<-4.5[/tex]

This means that solution of our inequalities is x values greater than [tex]-12[/tex] and less than [tex]-4.5[/tex].

We know that integers between [tex]-12[/tex] and [tex]-4.5[/tex] are: [tex]-11,-10,-9,-8,7,-6,-5[/tex].

Therefore, our solution would be [tex]x=\{-11,-10,-9,-8,7,-6,-5\}[/tex].

JeanaShupp

Answer: -11, -10,- 9, -8, -7, -6, -5

Step-by-step explanation:

The given inequalities:

[tex]2x + 9 < 0\quad...(i)\\x>-12\quad...(ii)[/tex]

First we solve inequality (i) to check the value of x that satisfy this inequality alone,

1) Add -9 on both sides , we get

[tex]2x<-9[/tex]

2) Divide both sides by 2, we get

[tex]x<\frac{-9}{2}\ or\ x<-4.5\quad...(iii)[/tex]

Now , from (ii) and (satisfy) , the common values of x that these inequalities are

[tex]-12<x<-4.5[/tex]

i.e. x takes the values between -12 and -4.5.

So , the list of integers that satisfy both these inequalities = -11, -10,- 9, -8, -7, -6, -5

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