https://file.aiquickdraw.com/mathbot/file/1727066153975frqjul39.jpg

The question asks, "Which inequality is true when the value of \( q = 18 \)?"

We are given four inequalities:

1. \( -q + 6 > 3 \)
2. \( -q + 6 < 3 \)
3. \( -q + 6 > -3 \)
4. \( q + 6 < 3 \)

Now, let's substitute \( q = 18 \) into each inequality to check which one is true:

1. \( -q + 6 > 3 \)
   \[
   -(18) + 6 > 3 \quad \Rightarrow \quad -18 + 6 > 3 \quad \Rightarrow \quad -12 > 3
   \]
   This is **false**.

2. \( -q + 6 < 3 \)
   \[
   -(18) + 6 < 3 \quad \Rightarrow \quad -18 + 6 < 3 \quad \Rightarrow \quad -12 < 3
   \]
   This is **true**.

3. \( -q + 6 > -3 \)
   \[
   -(18) + 6 > -3 \quad \Rightarrow \quad -18 + 6 > -3 \quad \Rightarrow \quad -12 > -3
   \]
   This is **false**.

4. \( q + 6 < 3 \)
   \[
   18 + 6 < 3 \quad \Rightarrow \quad 24 < 3
   \]
   This is **false**.

The correct inequality is the second one: **\( -q + 6 < 3 \)**.

Would you like further details on solving inequalities or have any questions?

Here are some related questions you might consider:
1. What is the process of solving inequalities with variables?
2. How do inequality symbols change when multiplying or dividing by negative numbers?
3. What is the significance of testing boundary values in inequalities?
4. Can you explain how to graph inequalities on a number line?
5. What happens if we switch the direction of an inequality? How does the solution change?

**Tip:** Always double-check the inequality symbol when performing operations like multiplying or dividing by negative numbers!

Which inequality is true when the value of q is 18?

Determine which inequality holds true when substituting q = 18 in various algebraic inequalities. Explore methods to test inequalities and solve step-by-step for Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation