Question

Radical Equations Quick Check
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.