Kris solved the radical equation √15−x+x=3

Question

and found that x=−1
or x=6
.

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

(1 point)
Responses

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

x=1
x equals 1

x=−1
x equals negative 1

x=−1
or x=6

Answer 1

To determine the correct statement regarding the solution set of the radical equation \( \sqrt{15 - x} + x = 3 \), we can verify Kris's solutions:

1. Checking \( x = -1 \): \[ \sqrt{15 - (-1)} + (-1) = \sqrt{15 + 1} - 1 = \sqrt{16} - 1 = 4 - 1 = 3 \] This satisfies the equation.

2. Checking \( x = 6 \): \[ \sqrt{15 - 6} + 6 = \sqrt{9} + 6 = 3 + 6 = 9 \] This does NOT satisfy the equation.

Given that only \( x = -1 \) satisfies the original equation, the correct statement describing the solution set is:

\( x = -1 \) or \( x = 6 \) is incorrect because only \( x = -1 \) is valid.

The correct response is: \( x = -1 \) or \( x = 6 \) is not suitable. The only correct solution is: \( x = -1 \).