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)
Responses

Answer 1

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

Starting with the original equation:

\[
3x^2 + 7 = 10
\]

Subtract 7 from both sides:

\[
3x^2 = 3
\]

Now divide by 3:

\[
x^2 = 1
\]

Taking the square root of both sides gives:

\[
x = \pm 1
\]

Thus, the solutions are:

\[
x = -1 \quad \text{and} \quad x = 1
\]

In set notation, this can be expressed as:

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

So the final answer is:

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