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Answer :
To classify the equation [tex]\(33x + 99 = 33x - 99\)[/tex] as having one solution, no solution, or infinitely many solutions, follow these steps:
1. Simplify the Equation: Start by subtracting [tex]\(33x\)[/tex] from both sides of the equation to isolate the constant terms. This helps to see if the equation is consistent or contradictory without involving the variable [tex]\(x\)[/tex].
[tex]\[
33x + 99 - 33x = 33x - 99 - 33x
\][/tex]
This simplifies to:
[tex]\[
99 = -99
\][/tex]
2. Analyze the Result: After simplification, we have the equation [tex]\(99 = -99\)[/tex]. This is a false statement, as 99 is not equal to -99.
3. Conclusion: Since we ended up with a false statement, it means there is no possible value of [tex]\(x\)[/tex] that can satisfy the equation. When an equation simplifies to a contradiction, it indicates that there are no solutions that can make the equation true.
Therefore, the given equation [tex]\(33x + 99 = 33x - 99\)[/tex] has no solution.
1. Simplify the Equation: Start by subtracting [tex]\(33x\)[/tex] from both sides of the equation to isolate the constant terms. This helps to see if the equation is consistent or contradictory without involving the variable [tex]\(x\)[/tex].
[tex]\[
33x + 99 - 33x = 33x - 99 - 33x
\][/tex]
This simplifies to:
[tex]\[
99 = -99
\][/tex]
2. Analyze the Result: After simplification, we have the equation [tex]\(99 = -99\)[/tex]. This is a false statement, as 99 is not equal to -99.
3. Conclusion: Since we ended up with a false statement, it means there is no possible value of [tex]\(x\)[/tex] that can satisfy the equation. When an equation simplifies to a contradiction, it indicates that there are no solutions that can make the equation true.
Therefore, the given equation [tex]\(33x + 99 = 33x - 99\)[/tex] has no solution.
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