1) To solve the inequality 15 - |z| ≥ 0, we first isolate the absolute value term by moving the constant to the other side:
|z| ≤ 15
Now we consider two cases for the absolute value:
Case 1: If z is positive or zero (|z| = z),z ≤ 15
Case 2: If z is negative (|z| = -z),-z ≤ 15z ≥ -15
Therefore, the solution to the inequality 15 - |z| ≥ 0 is z ≤ 15 or z ≥ -15.
2) To solve the inequality |z| - 7 > 0, we first isolate the absolute value term by moving the constant to the other side:
|z| > 7
Case 1: If z is positive or zero (|z| = z),z > 7
Case 2: If z is negative (|z| = -z),-z > 7z < -7
Therefore, the solution to the inequality |z| - 7 > 0 is z < -7 or z > 7.
1) To solve the inequality 15 - |z| ≥ 0, we first isolate the absolute value term by moving the constant to the other side:
|z| ≤ 15
Now we consider two cases for the absolute value:
Case 1: If z is positive or zero (|z| = z),
z ≤ 15
Case 2: If z is negative (|z| = -z),
-z ≤ 15
z ≥ -15
Therefore, the solution to the inequality 15 - |z| ≥ 0 is z ≤ 15 or z ≥ -15.
2) To solve the inequality |z| - 7 > 0, we first isolate the absolute value term by moving the constant to the other side:
|z| > 7
Now we consider two cases for the absolute value:
Case 1: If z is positive or zero (|z| = z),
z > 7
Case 2: If z is negative (|z| = -z),
-z > 7
z < -7
Therefore, the solution to the inequality |z| - 7 > 0 is z < -7 or z > 7.