Question

How do I express the solutions to the equation 3x^2 + 7 = 10, which are -1 and 1, in set notation?

Answer 1

To express the solutions to the equation \( 3x^2 + 7 = 10 \) in set notation, you first need to find the solutions.

1. Start by solving the equation:
\[
3x^2 + 7 = 10
\]
Subtract 7 from both sides:
\[
3x^2 = 3
\]
Now, divide both sides by 3:
\[
x^2 = 1
\]
Take the square root of both sides:
\[
x = \pm 1
\]

The solutions are \( x = -1 \) and \( x = 1 \).

2. In set notation, you can express the set of solutions as:
\[
\{-1, 1\}
\]

Thus, the solutions to the equation expressed in set notation are:
\[
\{-1, 1\}
\]