High School

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

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

Answer :

To determine the number of solutions for the equation [tex]\(33x + 99 = 33x - 99\)[/tex], follow these steps:

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

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

This simplifies to:

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

2. Analyze the resulting equation.

The equation [tex]\(99 = -99\)[/tex] is clearly false because 99 is not equal to -99. This shows that there is a contradiction in the equation.

3. Classify the equation based on the outcome.

Since the equation simplifies to a false statement, it means that there is no possible value of [tex]\(x\)[/tex] that can satisfy the original equation. Hence, the equation has no solution.

In conclusion, the equation is classified as having no solution.