https://file.aiquickdraw.com/mathbot/file/1727066388526lj5duprt.jpg

To determine which inequality is true when \( a = -8 \), let's substitute \( a = -8 \) into each inequality and check which one holds true:

### 1. \( -a + 3 \leq 5 \)
Substitute \( a = -8 \):
\[
-(-8) + 3 \leq 5 \implies 8 + 3 \leq 5 \implies 11 \leq 5
\]
This is **false**.

### 2. \( -a + 3 \geq -5 \)
Substitute \( a = -8 \):
\[
-(-8) + 3 \geq -5 \implies 8 + 3 \geq -5 \implies 11 \geq -5
\]
This is **true**.

### 3. \( -a + 3 \leq -5 \)
Substitute \( a = -8 \):
\[
-(-8) + 3 \leq -5 \implies 8 + 3 \leq -5 \implies 11 \leq -5
\]
This is **false**.

### 4. \( a + 3 \geq 5 \)
Substitute \( a = -8 \):
\[
-8 + 3 \geq 5 \implies -5 \geq 5
\]
This is **false**.

### Conclusion:
The correct inequality is **\( -a + 3 \geq -5 \)**, which is the second option.

---

Would you like more details or have any questions on this?

Here are 5 related questions to explore:
1. What are the rules for solving inequalities with variables?
2. How does flipping the inequality sign work when multiplying or dividing by negative numbers?
3. How do you graph inequalities on a number line?
4. What is the difference between strict (\(<\), \(>\)) and non-strict inequalities (\(\leq\), \(\geq\))?
5. How do compound inequalities work?

**Tip:** When solving inequalities, always be cautious when multiplying or dividing by a negative number as it flips the inequality sign!

Which inequality is true when the value of a is -8?

Learn how to solve inequalities by substituting a = -8 into various expressions and determining which inequality holds true. This example covers key algebraic concepts related to inequalities. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation