Final answer:
The absolute value inequality | – z|≤9 can be solved by creating two scenarios, resulting in the compound inequality −9 ≤ z ≤ 9, which indicates that z can be any number between -9 and 9, including the endpoints.
Step-by-step explanation:
When given the inequality | – z|≤9, we can express it in the form of a compound inequality to show the range of values that z can take. The absolute value inequality indicates that the distance between z and the number 0 on the number line is less than or equal to 9. Solving the absolute value inequality involves considering both the positive and negative scenarios.
To solve | – z|≤9, we need to split it into two separate inequalities:
• For the positive scenario, –z ≤ 9, which simplifies to z ≥ –9.
• For the negative scenario, –z ≥ –9, which simplifies to z ≤ 9.
By combining these two inequalities, we can express the solution as a compound inequality: −9 ≤ z ≤ 9. This tells us that z can be any number between and including –9 and 9.