-10
-5
0
5
-2
Select the values that make the inequality g, ≥, minus, 2g≥−2 true.
(Numbers written in order from least to greatest going across.)
Answer
Attempt 1 out of 2
 -10	 -7	 -5
 -3	 -2.1	 -2.01
 -2.001	 -2	 -1.999
 -1.99	 -1.9	 -1
 1	 3	 6Submit Answer
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To solve the inequality \( g \geq -2g \geq -2 \), we need to break it down and solve for \( g \).

1. **Step 1: Analyze the inequality**
   \[
   g \geq -2g \geq -2
   \]
   This inequality can be written as two parts:
   \[
   -2g \geq -2 \quad \text{(left inequality)}
   \]
   and
   \[
   g \geq -2g \quad \text{(right inequality)}.
   \]

2. **Step 2: Solve the left inequality**
   \[
   -2g \geq -2.
   \]
   Divide both sides by -2, remembering to reverse the inequality sign:
   \[
   g \leq 1.
   \]

3. **Step 3: Solve the right inequality**
   \[
   g \geq -2g.
   \]
   Add \( 2g \) to both sides:
   \[
   3g \geq 0.
   \]
   Divide by 3:
   \[
   g \geq 0.
   \]

4. **Step 4: Combine the results**
   The solutions from both inequalities are:
   \[
   0 \leq g \leq 1.
   \]
   So \( g \) must be between 0 and 1, inclusive.

5. **Step 5: Select the correct values**
   From the provided options, the values that satisfy \( 0 \leq g \leq 1 \) are:
   \[
   0, 1.
   \]

Thus, the correct answers are **0** and **1**.

Would you like more details or have any questions?

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Here are 5 related questions to expand on this concept:
1. How do you solve a compound inequality with three parts?
2. What happens when you divide an inequality by a negative number?
3. Can you graph the solution to the inequality \( 0 \leq g \leq 1 \)?
4. How do you verify if a value is a solution to an inequality?
5. How would the solution change if the inequality was strict (e.g., \( g > -2g > -2 \))?

**Tip:** Always remember to reverse the inequality sign when multiplying or dividing by a negative number.

Select the values that make the inequality g ≥ -2 true.

Learn how to solve the inequality g ≥ -2, with a step-by-step explanation. Understand how to manipulate inequalities and find the correct solution from a list of values. This problem is ideal for students in Grades 6-8, focusing on inequalities and their properties.

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