Question

List the integers that satisfy both these inequalities. 2x + 9 < 0 x>-12

Answer 1

We have been given two inequalities $2x+9$ and $x>-12$. We are asked to find the integers that satisfy both inequalities.

Let us solve for our 1st inequality.

$2x+9-9$

$2x$

$\frac{2x}{2}$

$x$

Upon combining our both inequalities, we will get:

$-12$

This means that solution of our inequalities is x values greater than $-12$ and less than $-4.5$.

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

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

Answer 2

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

Step-by-step explanation:

The given inequalities:

$2x + 9 < 0\quad...(i)\\x>-12\quad...(ii)$

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

1) Add -9 on both sides , we get

$2x$

2) Divide both sides by 2, we get

$x$

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

$-12$

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