Question
After solving the algebraic equation \( 6(y-4)=6(y+4) \), you end up with \( -24=24 \). What does this mean? Oy= all real numbers O \( y=-24 \) and 24 There are no solutions to this equation. You made a mistake in your algebra
Ask by Pearson Donnelly. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
There are no solutions to the equation.
Solution
When you solve the equation \( 6(y - 4) = 6(y + 4) \), let's go through the steps:
1. **Expand both sides:**
\[
6y - 24 = 6y + 24
\]
2. **Subtract \( 6y \) from both sides:**
\[
-24 = 24
\]
This leads to a statement that is clearly false (\( -24 \neq 24 \)). This kind of result indicates that there is **no possible value of \( y \)** that can satisfy the original equation.
**Therefore, the correct conclusion is:**
**There are no solutions to this equation.**
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
When you simplify the equation \( 6(y-4)=6(y+4) \), you can divide both sides by 6 (as long as 6 is not zero, which it isn't), leading you to \( y-4 = y+4 \). Simplifying this results in \( -4 = 4 \), which indicates an inconsistency. This means that the original equation has no solutions, as it implies a false statement. The takeaway here is that when you reach a conclusion like \( -24 = 24 \) in algebra, it indicates that the equation represents parallel lines that never intersect. Thus, there are no values of \( y \) that satisfy this equation, solidifying your conclusion that there are no solutions. Keep this in mind as it’s a key concept in understanding equations in algebra!
