Answered

Westonci.ca makes finding answers easy, with a community of experts ready to provide you with the information you seek. Ask your questions and receive accurate answers from professionals with extensive experience in various fields on our platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

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]
We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.