College

Classify the equation [tex]33x + 99 = 33x - 99[/tex] as having one solution, no solution, or infinitely many solutions.

Given:
[tex]\[

33x + 99 = 33x - 99

\][/tex]

Since 99 is not equal to -99, the equation has no solution.

Answer :

To solve and classify the equation [tex]\( 33x + 99 = 33x - 99 \)[/tex], let's follow these steps:

1. Start with the given equation:

[tex]\[
33x + 99 = 33x - 99
\][/tex]

2. Subtract [tex]\( 33x \)[/tex] from both sides of the equation to try to simplify it further:

[tex]\[
33x + 99 - 33x = 33x - 99 - 33x
\][/tex]

3. Simplify both sides:

[tex]\[
99 = -99
\][/tex]

4. Analyze the result:

You end up with the statement [tex]\( 99 = -99 \)[/tex]. This is a false statement. Since both sides of the equation cannot be equal, there is no possible solution for [tex]\( x \)[/tex] that can satisfy the equation.

5. Conclusion:

Because the equation simplifies to a false statement, there are no values for [tex]\( x \)[/tex] that make the equation true. Therefore, the equation has no solution.