Question

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Question 1
Consider the inequality.

−4x−5<31

Correctly order the steps used to solve the inequality.

(1 point)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Step 1.
Step 2.
Step 3.
Question 2
What is the solution set for −4x−5<31
?(1 point)
Responses

x<−9
x<−9

x>−9
x is greater than negative 9

x>9
x is greater than 9

x<9
x<9
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page 4 of 4

Answer 1

To solve the inequality \(-4x - 5 < 31\), we can break it down into the following steps:

### Steps to Solve the Inequality:

**Step 1:** Add 5 to both sides of the inequality.
\[
-4x - 5 + 5 < 31 + 5
\]
This simplifies to:
\[
-4x < 36
\]

**Step 2:** Divide both sides by -4. Remember that when you divide by a negative number, you must reverse the inequality sign.
\[
x > \frac{36}{-4}
\]
This simplifies to:
\[
x > -9
\]

### The correct order of steps:
- **Step 1:** Add 5 to both sides.
- **Step 2:** Divide by -4 and reverse the inequality.

### Question 2: What is the solution set for \(-4x - 5 < 31\)?

The correct response is:
- \(x > -9\) (or "x is greater than negative 9").

So, the solution set is: **x > -9**.