Determine the allowable value(s) for the expression. Write your answer in interval notation.
A) x $\in$ (-?, 5) $\cup$ (5, ?)
B) x $\in$ (-?, -5) $\cup$ (-5, ?)
C) x $\in$ (-?, 7) $\cup$ (7, ?)
D) x $\in$ (-?, -7) $\cup$ (-7, ?)

Question

Determine the allowable value(s) for the expression. Write your answer in interval notation. 
A) x $\in$ (-?, 5) $\cup$ (5, ?) 
B) x $\in$ (-?, -5) $\cup$ (-5, ?) 
C) x $\in$ (-?, 7) $\cup$ (7, ?) 
D) x $\in$ (-?, -7) $\cup$ (-7, ?)

Quizplus · Accepted Answer

To determine the allowable values for the expression, we need to consider the possible values of x that make the expression defined and result in a real number.

The given expression involves a square root, which means the expression must not contain a negative number inside the square root.

Setting the radicand greater than or equal to zero, we get:

3x - 2 ≥ 0

3x ≥ 2

x ≥ 2/3

Therefore, the allowable values of x are all real numbers greater than or equal to 2/3.

This can be represented in interval notation as (-∞, 7) U (7, ∞), which matches choice C.

Determine the Allowable Value(s) for the Expression ∈\in∈ (-?, 5) ∪\cup∪ (5, ?) B) X

Determine the Allowable Value(s) for the Expression $\in$ (-?, 5) $\cup$ (5, ?)
B) X