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------------------------------------------------ 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]

Subtract [tex]33x[/tex] from both sides:
[tex]99 = -99[/tex]

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

To classify the equation [tex]\(33x + 99 = 33x - 99\)[/tex], we need to analyze whether it has one solution, no solution, or infinitely many solutions.

1. Subtract [tex]\(33x\)[/tex] from both sides of the equation:

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

This simplifies the equation to:

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

2. Analyze the resulting statement:

The equation [tex]\(99 = -99\)[/tex] is clearly not true because 99 is not equal to -99.

3. Determine the number of solutions:

Since the statement [tex]\(99 = -99\)[/tex] is false, it means that there is no value of [tex]\(x\)[/tex] that will satisfy the original equation. Therefore, the equation has no solutions.

In conclusion, the given equation [tex]\(33x + 99 = 33x - 99\)[/tex] has no solutions.