Solve the absolute value inequality. Graph the solution set on a real number line.
StartAbsoluteValue 5 x plus 4 EndAbsoluteValue less than minus 65x+4<−6
Question content area bottom
Part 1
Select the correct choice below and fill in any answer boxes within your choice.
A.
The solution set is enter your response here.
​(Type your answer in interval​ notation.)
B.
The solution is the empty set.
Part 2
Choose the correct graph of the solution set below.

We are tasked with solving the absolute value inequality:

\[
|5x + 4| < -6
\]

### Step 1: Analyze the inequality

First, recognize that the absolute value of any expression is always **non-negative** (i.e., it is always greater than or equal to 0). Therefore, it can never be less than a negative number. Here, the right-hand side of the inequality is -6, a negative number. 

\[
|5x + 4| \geq 0 \quad \text{for all values of } x
\]

Since the inequality is asking whether an absolute value expression can be less than a negative number (which is impossible), there is no solution to this inequality.

### Step 2: Conclusion

The solution is the **empty set**. 

Thus, the correct answer is:

\[
\text{B. The solution is the empty set.}
\]

### Step 3: Graph the solution

Since there is no solution, the graph on a real number line would be empty—there are no values of \(x\) that satisfy this inequality.

---

Do you want more details, or have any questions about this?  
Here are 5 related questions that expand on this concept:

1. What happens when the inequality involves \( |5x + 4| \leq 6 \)?
2. How would the solution change if the right side were a positive number, like 6?
3. How do we solve inequalities involving \( |5x + 4| > 6 \)?
4. How can we graph an absolute value inequality on a number line for different cases?
5. What are the properties of absolute value functions?

**Tip**: Absolute value inequalities involving a negative number on the right side often have no solutions because absolute values are always non-negative.

Solve the absolute value inequality. Graph the solution set on a real number line. |5x + 4| < -6

Learn how to solve and graph the absolute value inequality |5x + 4| < -6. This problem demonstrates why absolute values cannot be less than negative numbers, leading to an empty solution set. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation