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List the integers that satisfy both of these inequalities:
[tex]\[
\begin{array}{c}
2x + 9 \ \textless \ 0 \\
x \ \textgreater \ -12
\end{array}
\][/tex]

Put the answers on one line.

Sagot :

GinnyAnswer
To find the integers that satisfy both inequalities \(2x + 9 < 0\) and \(x > -12\), follow these detailed steps:

### 1. Solve the first inequality: \(2x + 9 < 0\)

First, isolate \(x\):

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

Subtract 9 from both sides:

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

Divide both sides by 2:

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

Since \(-\frac{9}{2}\) is equivalent to \(-4.5\), we have:

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

### 2. Solve the second inequality: \(x > -12\)

This inequality is already solved:

[tex]\[ x > -12 \][/tex]

### 3. Combine the inequalities

Now we need to find the intersection of these two solutions:

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

### 4. Identify the integers in the solution set

Integers are whole numbers. Within the interval \(-12 < x < -4.5\), the integers are:

[tex]\[ -11, -10, -9, -8, -7, -6, -5 \][/tex]

Thus, the integers that satisfy both inequalities are:

[tex]\[ -11, -10, -9, -8, -7, -6, -5 \][/tex]
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