Pregunta
7. Dok solved an equation tor s. tile work te shown betow. How thany soluttons are there to thte bqumton? \[ \begin{array}{c} 3 x-6=3(x-2) \\ 3 x-6=3 x-6 \\ 3 x-3 x-6=3 x-3 x-6 \\ 6=-6 \end{array} \]
Ask by Tran Hilton. in the United States
Jan 23,2025
Solución de tutoría real
Respuesta verificada por el tutor
Responder
There are infinitely many solutions to the equation.
Solución
Let's analyze the steps shown in the work Dok provided to solve the equation for \( x \):
1. The original equation is:
\[
3x - 6 = 3(x - 2)
\]
2. Expanding the right side:
\[
3x - 6 = 3x - 6
\]
3. The next step shows:
\[
3x - 3x - 6 = 3x - 3x - 6
\]
This simplifies to:
\[
-6 = -6
\]
The final statement \( -6 = -6 \) is a true statement, which indicates that the original equation is an identity. This means that the equation holds true for all values of \( x \).
### Conclusion:
Since the equation is true for all \( x \), there are infinitely many solutions to the equation.
Revisado y aprobado por el equipo de tutoría de UpStudy
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Simplifique esta solución Bonus Knowledge
Dok's equation ultimately simplifies to \(6 = -6\), which is a contradictory statement. Whenever the simplification of an equation leads to a false statement like this, it indicates that there are no values of \(x\) that can satisfy the equation. In essence, this means the equation has no solutions. This type of outcome is common in algebra, and it serves as a reminder to double-check each step in your calculations. A common mistake is assuming there is always an answer; instead, understanding when an equation is inconsistent prepares you for more complex problem-solving scenarios. Always keep an eye out for contradictions while solving!
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