Solve for z.z2–75≥–74

The given inequality is z^2 - 75 ≥ -74.

Step 1: Add 75 to both sides of the inequality to isolate z^2 on one side:

z^2 ≥ -74 + 75

Step 2: Simplify the right side of the inequality:

z^2 ≥ 1

Step 3: Take the square root of both sides of the inequality. Remember that when you take the square root of both sides of an inequality, you get two solutions: one positive and one negative.

z ≥ √1 and z ≤ -√1

Step 4: Simplify the square roots:

z ≥ 1 and z ≤ -1

So the solution to the inequality z^2 - 75 ≥ -74 is z ≥ 1 and z ≤ -1.