Question
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
Real Tutor Solution
Tutor-Verified Answer
Answer
There is no solution.
Solution
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.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution 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!
