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

Given:

[tex]
\begin{array}{c}
33x + 99 = 33x - 99 \\
33x - 33x + 99 = 33x - 33x - 99 \\
99 \neq -99
\end{array}
[/tex]

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

Answer :

To classify the given equation [tex]\(33x + 99 = 33x - 99\)[/tex], let's solve it step by step:

1. Start with the given equation:
[tex]\[
33x + 99 = 33x - 99
\][/tex]

2. Subtract [tex]\(33x\)[/tex] from both sides to eliminate the [tex]\(x\)[/tex] terms:
[tex]\[
33x + 99 - 33x = 33x - 99 - 33x
\][/tex]

This simplifies to:
[tex]\[
99 = -99
\][/tex]

3. Analyze the resulting statement:
- We end up with [tex]\(99 = -99\)[/tex], which is a contradiction because 99 is not equal to -99.

Since the statement is false and we cannot find any [tex]\(x\)[/tex] that makes the original equation true, this means the equation has no solutions. This tells us that there is no value of [tex]\(x\)[/tex] that will satisfy the equation. Therefore, the equation is classified as having no solution.