Question

Juan Anisha and gesilly 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

Answer 1

It seems like Juan, Anisha, and Gesilly are discussing how to solve the inequality \( \frac{5}{6}x \leq -10 \). To clarify, the rule about reversing the inequality symbol only applies when you multiply or divide both sides of an inequality by a negative number. Let's go step by step through the process of solving the inequality:

1. Start with the initial inequality:
\[
\frac{5}{6}x \leq -10
\]

2. To isolate \( x \), multiply both sides by \( \frac{6}{5} \). Importantly, since \( \frac{6}{5} \) is a positive number, the direction of the inequality does not change:
\[
x \leq -10 \cdot \frac{6}{5}
\]

3. Calculate the right side:
\[
x \leq -12
\]

In solving this inequality, Juan’s statement about needing to reverse the inequality symbol due to a negative sign is incorrect because we did not multiply or divide both sides by a negative number at any point in our solution. The inequality only reverses when you multiply or divide by a negative value, which was not done here.

Thus, the final solution is:
\[
x \leq -12
\]

This means that Juan, Anisha, and Gesilly should conclude that \( x \) can take any value less than or equal to -12.