Which of the following values are solutions to the inequality 5, x, plus, 5, is greater than or equal to, minus, 9, question mark5x+5≥−9?
I., 4, II., 6, III., 1
I.4II.6III.1

We are given the inequality \( 5x + 5 \geq -9 \) and need to determine which of the values \( 4 \), \( 6 \), and \( 1 \) are solutions.

### Step 1: Solve the inequality

\[
5x + 5 \geq -9
\]

Subtract 5 from both sides:

\[
5x \geq -9 - 5
\]

\[
5x \geq -14
\]

Now, divide both sides by 5:

\[
x \geq \frac{-14}{5}
\]

\[
x \geq -2.8
\]

### Step 2: Test the values

Now, we test each of the given values to see if they satisfy the inequality \( x \geq -2.8 \).

- **I. \( 4 \)**: \( 4 \geq -2.8 \) is true.
- **II. \( 6 \)**: \( 6 \geq -2.8 \) is true.
- **III. \( 1 \)**: \( 1 \geq -2.8 \) is true.

### Conclusion:
All three values \( 4 \), \( 6 \), and \( 1 \) are solutions to the inequality. So, the correct answer is **I., II., and III.**.

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

Here are 5 follow-up questions for further practice:

1. How would you solve the inequality \( 3x - 2 \leq 7 \)?
2. Can you graph the inequality \( 5x + 5 \geq -9 \)?
3. What are the properties of inequalities when multiplying or dividing by a negative number?
4. How would you represent the solution \( x \geq -2.8 \) on a number line?
5. What happens if we change the inequality to \( 5x + 5 > -9 \)?

**Tip**: Always flip the inequality sign when multiplying or dividing both sides by a negative number.

Which of the following values are solutions to the inequality 5x + 5 ≥ -9? I. 4, II. 6, III. 1

Explore how to solve the inequality 5x + 5 ≥ -9 and determine which of the values 4, 6, and 1 are solutions. This problem involves key algebraic concepts and demonstrates step-by-step inequality solving. Perfect for students in Grades 6-8.

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