Questions: Solve the compound inequality. Graph the solution set and write it in interval notation. x < -4 and x < 4 Write the solution set in interval notation. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is . (Type your answer in interval notation. Simplify your answer.) B. The solution set is ∅.

Solution Steps

The given compound inequality is \( x \leq -4 \) and \( x < 4 \).

• For \( x \leq -4 \): This means all values of \( x \) that are less than or equal to -4.
• For \( x < 4 \): This means all values of \( x \) that are less than 4.

Since the compound inequality uses "and," we need the intersection of the two sets:

• The intersection of \( x \leq -4 \) and \( x < 4 \) is \( x \leq -4 \).

The correct graph should show all values less than or equal to -4. This corresponds to option A in the provided choices.

The interval notation for \( x \leq -4 \) is \( (-\infty, -4] \).

Final Answer