Question

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

Answer 1

To find the solution to the equation \( 3x^2 + 7 = 10 \), we first simplify the equation:

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 means the solutions are \( x = -1 \) and \( x = 1 \).

Using set notation, we express the solution as:
\[
\{ -1, 1 \}
\]

So, the solution to the equation \( 3x^2 + 7 = 10 \) in set notation is \( \{ -1, 1 \} \).