Question

The values −1 and 1 make the equation 3x2+7=10 true. Use set notation to express the solution to the equation.(1 point)

Answer 1

To express the solution to the equation \(3x^2 + 7 = 10\) in set notation, we first solve for \(x\):

1. Subtract 7 from both sides:
\[
3x^2 = 10 - 7
\]
\[
3x^2 = 3
\]

2. Divide both sides by 3:
\[
x^2 = 1
\]

3. Take the square root of both sides:
\[
x = \pm 1
\]
This gives us the solutions \(x = 1\) and \(x = -1\).

Now we can express the solution in set notation:

\[
\{ -1, 1 \}
\]

So the solution set is \( \{ -1, 1 \} \).