Question

Set up an inequality showing that the radicand cannot be negative. a. 3t-9≥0 b. 3t+9≥0 c. 3t≥0 d. t≥0

Answer 1

The correct inequality to ensure the radicand is non-negative, and thereby allowing for a real number solution when taking the square root, is (a) 3t-9≥0.

Step-by-step explanation:

To set up an inequality showing that the radicand cannot be negative, you need to identify the expression that's inside the square root (the radicand) and ensure it is greater than or equal to zero. In the inequality examples provided, the correct answer should be one that prevents the radicand from being negative to allow for a real number solution when taking the square root.

Looking at the options provided:

a. 3t-9≥0;

b. 3t+9≥0;

c. 3t≥0;

d. t≥0 - the correct inequality would be the one where '3t-9' is the radicand, since this is the expression that would be under the square root in a radical equation. Therefore, the correct inequality ensuring the radicand is non-negative would be:

(a) 3t-9≥0.