High School

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

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

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

Answer :

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

1. Examine the Structure of the Equation:
The equation is [tex]\(33x + 99 = 33x - 99\)[/tex]. Notice that both sides have the term [tex]\(33x\)[/tex].

2. Simplify by Removing the Variable Term:
Subtract [tex]\(33x\)[/tex] from both sides of the equation. This step removes the [tex]\(33x\)[/tex] terms from both sides:

[tex]\[
33x + 99 - 33x = 33x - 99 - 33x
\][/tex]
Which simplifies to:
[tex]\[
99 = -99
\][/tex]

3. Analyze the Simplified Equation:
We end up with a statement that reads [tex]\(99 = -99\)[/tex]. Since this is a false statement (99 is not equal to -99), it means that the original equation has no values of [tex]\(x\)[/tex] that can satisfy it.

4. Conclusion:
Since we reached a false statement after simplifying, the equation [tex]\(33x + 99 = 33x - 99\)[/tex] has no solution.

In summary, since eliminating the variable term leaves us with an impossible statement, this tells us that the equation has no solution.