Questions: Solve the compound inequality. Graph the solution set, and write the solution set in interval notation if possible. (a) z ≤ -3 and z > -5 (b) z ≤ -3 or z > -5

Transcript text: Solve the compound inequality. Graph the solution set, and write the solution set in interval notation if possible. (a) $z \leq-3$ and $z>-5$ (b) $z \leq-3$ or $z>-5$

Solution

Solution Steps

Step 1: Analyze the compound inequality

The given compound inequality is z ≤ -3 and z > -5. This means we're looking for values of _z_ that satisfy both conditions simultaneously.

Step 2: Determine the solution set

The inequality z ≤ -3 represents all numbers less than or equal to -3. The inequality z > -5 represents all numbers greater than -5. The overlap, or intersection, of these two sets is all numbers greater than -5 and less than or equal to -3.

Step 3: Write the solution in interval notation

In interval notation, this is represented as (-5, -3]. The parenthesis indicates -5 is not included, and the bracket indicates -3 is included.