Write the following as an inequality.w is greater than or equal to −5 and less than or equal to −1Use w only once in your inequality.

To express the given conditions using an inequality, we can summarize the statements as follows:

1. Break Down the Problem
   We need to translate two conditions into a single inequality. The conditions are:

   • $w$ is greater than or equal to $-5$
   • $w$ is less than or equal to $-1$

2. Relevant Concepts
   The concepts involve inequalities and how to express ranges using them. Specifically, since $w$ needs to satisfy both conditions, we will use compound inequalities.

3. Analysis and Detail
   We can combine the two conditions into a single inequality by ensuring that $w$ meets both criteria simultaneously. The first condition can be written as: $w \geq -5$ The second condition can be expressed as: $w \leq -1$ When we combine these, we create a compound inequality: $-5 \leq w \leq -1$ This notation captures that $w$ can take any value from $-5$ to $-1$, including both endpoints.

4. Verify and Summarize
   We verify that both endpoints are included in our expression, confirming that the representation of values of $w$ satisfies both conditions. The final inequality succinctly represents the range of $w$.

Final Answer

The inequality representing the conditions is: $-5 \leq w \leq -1$