the values -1 and 1 make the equation 3x^2 + 7 = 10 true. use set notation to express the solution to the equation

Answer 1

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

1. Start by simplifying the equation:

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

2. Subtract 7 from both sides:

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

\[ 3x^2 = 3 \]

3. Divide both sides by 3:

\[ x^2 = 1 \]

4. Take the square root of both sides:

\[ x = \pm 1 \]

This gives us two solutions: \( x = -1 \) and \( x = 1 \).

Now, we can express the solution set in set notation:

\[ { -1, 1 } \]

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