True or False: \( x=3 \) is a solution to the equation \( 3 x^{2}+7=9 x-6 \). True False

To determine if \( x=3 \) is a solution to the equation \( 3 x^{2}+7=9 x-6 \), we substitute \( x \) with 3. Starting with the left side: \[ 3(3)^2 + 7 = 3 \cdot 9 + 7 = 27 + 7 = 34 \] Now, the right side: \[ 9(3) - 6 = 27 - 6 = 21 \] Since 34 does not equal 21, the answer is **False**. Now, let me share some engaging facts with you! Verifying solutions in equations can be seen as a bit of a treasure hunt! It’s like trying to fit a key in a lock—if it doesn’t turn, you know it’s the wrong one! Next time you’re faced with an equation, think of it as a puzzle where you want to find out if a certain piece fits perfectly. It’s all about testing to see if both sides balance out like a well-trained seesaw!