The given inequality is:

\[
- |z| > -5
\]

To solve for \( z \), follow these steps:

1. **Remove the negative sign** from both sides by dividing through by \(-1\). This reverses the inequality:

\[
|z| < 5
\]

2. **Interpret the absolute value inequality** \( |z| < 5 \). This means that the value of \( z \) lies between \(-5\) and \(5\):

\[
-5 < z < 5
\]

Thus, the solution is:

\[
z \in (-5, 5)
\]

Would you like more details or have any further questions?

---

Here are 5 related questions to explore:

1. What is the solution to \( |x| \leq 3 \)?
2. How do you solve inequalities involving absolute values with variables on both sides?
3. Can you explain how to graph the solution \( |z| < 5 \) on a number line?
4. How do you solve an absolute value equation like \( |x - 2| = 7 \)?
5. What happens if the inequality \( |z| > 5 \) was given instead?

**Tip:** When working with absolute value inequalities, remember to break the inequality into two parts—positive and negative—before solving!

Discover how to solve the absolute value inequality |-z| > -5 with a detailed step-by-step guide. This problem involves understanding the properties of inequalities and absolute values, leading to the solution z ∈ (-5, 5). Ideal for students in Grades 7-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation