Radical Equations Quick Check

Question

5 of 55 of 5 Items
Question
Kris solved the radical equation 15−x−−−−−√+x=3
and found that x=−1
or x=6
.

Which statement correctly describes the solution set of the radical equation?

(1 point)
Responses

x=1
x equals 1

x=−1
or x=6
x equals negative 1 or x equals 6

x=−1
x equals negative 1

x=−1
or x=−6

Answer 1

To determine which statement correctly describes the solution set of the radical equation \( \sqrt{15 - x} + x = 3 \), we need to check the validity of the solutions \( x = -1 \) and \( x = 6 \).

1. Check \( x = -1 \): \[ \sqrt{15 - (-1)} + (-1) = \sqrt{15 + 1} - 1 = \sqrt{16} - 1 = 4 - 1 = 3 \quad \text{(valid)} \]

2. Check \( x = 6 \): \[ \sqrt{15 - 6} + 6 = \sqrt{9} + 6 = 3 + 6 = 9 \quad \text{(invalid)} \]

Thus, only \( x = -1 \) is a valid solution. Therefore, the correct response that describes the solution set of the radical equation is:

x = -1

So, the final answer is: x=−1 x equals negative 1.