1. The problem asks us to study the inequality $x \leq -4$. 2. The inequality is already given: $x \leq -4$ means $x$ is less than or equal to $-4$. 3. To write this in interval notation, recall that $x \leq -4$ includes all values from negative infinity up to and including $-4$. 4. The interval notation for this is $$(-\infty, -4]$$ where the parenthesis on $-\infty$ means it is not included (since infinity is not a number), and the square bracket on $-4$ means $-4$ is included. Final answers: - Inequality: $x \leq -4$ - Interval notation: $$(-\infty, -4]$$