Final answer:
The expression √(7/6)x + 5 is undefined when x is less than -30/7 because the value under the square root (the radicand) would be negative. The correct choice given the student's options would be closest to (C) only when x is less than -30/7 instead of the provided value of -5/6.
Step-by-step explanation:
The expression √(7/6)x + 5 is undefined when the value under the square root, known as the radicand, is negative. Since the expression has the form of a square root of a linear function, we need to find the value of x that makes the radicand zero, which is the boundary of the domain where the expression is defined.
Let's set up the radicand to be equal to zero and solve for x:
- (7/6)x + 5 = 0
- (7/6)x = -5
- x = (-5)/(7/6)
- x = -5 * (6/7)
- x = -30/7 or approximately -4.2857
Thus, the expression is undefined for x < -30/7, which is equivalent to saying that x must be greater than -30/7 to be in the domain where the square root is defined. Therefore, the answer to the question when the expression is undefined is (C) only when x is less than -30/7, not when x is less than or equal to -5/6 as the student's options suggest.