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| – z|≤9 compound inequality form

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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.

User SimplyComplexable
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