Question
Juan Anisha and giselle are comparing their solutions to the inequality 5/6x is less than or equal to -10 Junie says that any quality symbol must be reversed because there is a negative sign in the equality
Answers
GPT-4o mini
It looks like there might be some confusion regarding how to solve an inequality with a negative number. Let's clarify the steps to solve the inequality \( \frac{5}{6}x \leq -10 \).
To solve this inequality, you want to isolate \( x \) on one side. Here’s how you can do it:
1. **Multiply both sides by 6** to eliminate the fraction:
\[
6 \cdot \frac{5}{6}x \leq 6 \cdot (-10)
\]
This simplifies to:
\[
5x \leq -60
\]
2. **Next, divide both sides by 5**:
\[
\frac{5x}{5} \leq \frac{-60}{5}
\]
This results in:
\[
x \leq -12
\]
In this particular case, there's no need to reverse the inequality symbol because we did not multiply or divide by a negative number when isolating \( x \). The rule about reversing the inequality symbol does apply when you multiply or divide by a negative number, but that did not happen here.
So the correct solution to the inequality \( \frac{5}{6}x \leq -10 \) is \( x \leq -12 \).
Junie's statement about needing to reverse the inequality symbol due to a negative sign does not apply in this situation, because we did not perform any operation that involves a negative number causing a need for a reversal. So, in this case, the interpretation is incorrect.
To solve this inequality, you want to isolate \( x \) on one side. Here’s how you can do it:
1. **Multiply both sides by 6** to eliminate the fraction:
\[
6 \cdot \frac{5}{6}x \leq 6 \cdot (-10)
\]
This simplifies to:
\[
5x \leq -60
\]
2. **Next, divide both sides by 5**:
\[
\frac{5x}{5} \leq \frac{-60}{5}
\]
This results in:
\[
x \leq -12
\]
In this particular case, there's no need to reverse the inequality symbol because we did not multiply or divide by a negative number when isolating \( x \). The rule about reversing the inequality symbol does apply when you multiply or divide by a negative number, but that did not happen here.
So the correct solution to the inequality \( \frac{5}{6}x \leq -10 \) is \( x \leq -12 \).
Junie's statement about needing to reverse the inequality symbol due to a negative sign does not apply in this situation, because we did not perform any operation that involves a negative number causing a need for a reversal. So, in this case, the interpretation is incorrect.