Pregunta
Question 3 * What is the solution, if any, to the equation \( 3(x-2)+4=3 x+6 \) ? \( x=0 \) \( x=8 \) There is no solution. There are an infinite number of solutions. Thint Then
Ask by Cox Sullivan. in the United States
Jan 24,2025
Solución de tutoría real
Respuesta verificada por el tutor
Responder
There is no solution.
Solución
Let's solve the equation step by step:
\[
3(x - 2) + 4 = 3x + 6
\]
1. **Expand the left side:**
\[
3(x - 2) + 4 = 3x - 6 + 4 = 3x - 2
\]
2. **Set the expanded left side equal to the right side:**
\[
3x - 2 = 3x + 6
\]
3. **Subtract \( 3x \) from both sides to eliminate \( x \):**
\[
-2 = 6
\]
This results in a **contradiction** because \(-2\) does not equal \(6\).
**Conclusion:** There is **no solution** to the equation.
**Correct Answer:**
There is no solution.
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Simplifique esta solución Bonus Knowledge
To solve the equation \( 3(x-2)+4=3x+6 \), we first expand and simplify the left side: \( 3x - 6 + 4 = 3x + 6 \), which simplifies to \( 3x - 2 = 3x + 6 \). Now, if we subtract \( 3x \) from both sides, we get \(-2 = 6\), which is a contradiction! That tells us that there's no value for \( x \) that can satisfy this equation. Whenever we encounter an equation that leads to a false statement like this, it indicates that there is no solution. It's like trying to fit a square peg in a round hole—sometimes, things just don’t match up!
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