https://file.aiquickdraw.com/mathbot/file/1730170161369599qa7tg.jpg

Let's examine each inequality to determine if the given values are solutions.

### Problem 1
**Is \( 12 \) a solution to \( -5x < 60 \)?**

1. Substitute \( x = 12 \) into the inequality:
   \[
   -5 \times 12 < 60
   \]
   \[
   -60 < 60
   \]
   This is true, so **Yes, 12 is a solution**.

### Problem 2
**Is \( -6 \) a solution to \( x + 4 \geq 2x \)?**

1. Substitute \( x = -6 \) into the inequality:
   \[
   -6 + 4 \geq 2 \times (-6)
   \]
   \[
   -2 \geq -12
   \]
   This is true, so **Yes, -6 is a solution**.

### Problem 3
**Is \( 5 \) a solution to \( 7(x - 1) \leq 4 \)?**

1. Substitute \( x = 5 \) into the inequality:
   \[
   7 \times (5 - 1) \leq 4
   \]
   \[
   7 \times 4 \leq 4
   \]
   \[
   28 \leq 4
   \]
   This is false, so **No, 5 is not a solution**.

### Summary of Answers:
1. Yes
2. Yes
3. No

Would you like further details or have any questions?

Here are 5 related questions to expand on these concepts:
1. How would you determine if a number is a solution to a quadratic inequality?
2. Can we check if multiple values are solutions at once, and how?
3. What steps are involved in solving compound inequalities?
4. How does one solve absolute value inequalities?
5. What happens when variables appear on both sides of an inequality?

**Tip:** When solving inequalities, always remember that multiplying or dividing by a negative number reverses the inequality sign.

Is 12 a solution to −5x < 60? Is -6 a solution to x + 4 ≥ 2x? Is 5 a solution to 7(x − 1) ≤ 4?

Learn how to determine if specific values satisfy inequalities like −5x < 60, x + 4 ≥ 2x, and 7(x − 1) ≤ 4. Follow step-by-step solutions to understand substitution in inequalities, properties of inequalities, and comparison techniques. Suitable for students in Grades 6-8.

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