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Write a compound inequality that represents each situation. Graph your solution.

all real numbers at least –8 and at most 0





–8 > x > 0

1 answer

To represent the situation where all real numbers are at least -8 and at most 0, we can write the compound inequality as follows:

\[ -8 \leq x \leq 0 \]

Explanation:

  • The symbol "≤" means "less than or equal to," indicating that -8 is included in the solution set.
  • The symbol "≤" in the other part of the inequality means that 0 is also included in the solution set.

Graphing the Solution:

  1. Draw a number line.
  2. Mark the points -8 and 0 on the number line.
  3. Use solid dots at -8 and 0 to indicate that these points are included in the solution.
  4. Shade the region between -8 and 0, including both endpoints.

Graph Representation:

<---|----|----|----|----|----|----|----|----|----|---->
   -9  -8   -7   -6   -5   -4   -3   -2   -1    0    
         ●=================●

Summary:

The correct compound inequality representing the given situation is \( -8 \leq x \leq 0 \), and the corresponding graph is shown above with included endpoints -8 and 0.