Questions: List the integers that make both inequalities true. x ≥ -8 and x ≥ 2 Choose the correct answer below, and if necessary, fill in the answer box(es) within your choice. A. All integers greater than or equal to satisfy both inequalities. (Type an integer or a decimal.) B. All integers less than or equal to satisfy both inequalities. (Type an integer or a decimal.) C. All integers greater than or equal to and less than or equal to satisfy both inequalities. (Type integers or decimals.) D. There are no integers that make both inequalities true.

List the integers that make both inequalities true. x ≥ -8 and x ≥ 2 Choose the correct answer below, and if necessary, fill in the answer box(es) within your choice. A. All integers greater than or equal to satisfy both inequalities. (Type an integer or a decimal.) B. All integers less than or equal to satisfy both inequalities. (Type an integer or a decimal.) C. All integers greater than or equal to and less than or equal to satisfy both inequalities. (Type integers or decimals.) D. There are no integers that make both inequalities true.
Transcript text: List the integers that make both inequalities true. \[ x \geq-8 \text { and } x \geq 2 \] Choose the correct answer below, and if necessary, fill in the answer box(es) within your choice. A. All integers greater than or equal to $\square$ satisfy both inequalities. (Type an integer or a decimal.) B. All integers less than or equal to $\square$ satisfy both inequalities. (Type an integer or a decimal.) C. All integers greater than or equal to $\square$ and less than or equal to $\square$ satisfy both inequalities. (Type integers or decimals.) D. There are no integers that make both inequalities true.
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Solution

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Solution Steps

Step 1: Analyze the inequalities

The given inequalities are: \[ x \geq -8 \quad \text{and} \quad x \geq 2 \] We need to find the integers that satisfy both inequalities simultaneously.

Step 2: Determine the overlapping range

The first inequality \(x \geq -8\) includes all integers greater than or equal to \(-8\). The second inequality \(x \geq 2\) includes all integers greater than or equal to \(2\). The overlapping range of these two inequalities is all integers greater than or equal to \(2\).

Step 3: Identify the correct choice

The correct choice is: \[ \text{A. All integers greater than or equal to } 2 \text{ satisfy both inequalities.} \]

Final Answer

\[ \boxed{\text{A. All integers greater than or equal to } 2 \text{ satisfy both inequalities.}} \]

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