Question

Dan, Sam, and Tom are comparing their solutions to the inequality 5/6x<=-10
Dan says the inequality symbol must be reversed because there is a negative sign in the inequality Sam says the multiplication property of inequality or division property of inequality must be applied. Tom says the inequality symbol stays the same
Which combination of people is correct
Dan and Sam
Tom and Sam
Tom and Dan
Tom, Dan and Sam

Answer 1

To solve the inequality \( \frac{5}{6}x \leq -10 \), let's first isolate \( x \).

1. Multiply both sides by \( \frac{6}{5} \) (the reciprocal of \( \frac{5}{6} \)):
\[
x \leq -10 \times \frac{6}{5}
\]
This gives:
\[
x \leq -12
\]

Now, let's evaluate the claims made by each person:

- **Dan** is incorrect. The inequality symbol does not need to be reversed simply because there is a negative number on the right side.

- **Sam** is correct in that the multiplication property of inequality is being applied when you multiply both sides by a positive number (the reciprocal \( \frac{6}{5} \)). However, he is not specifically saying that you need to reverse the inequality, which is what Dan is implying.

- **Tom** is also correct; the inequality symbol stays the same when multiplying or dividing by a positive number.

Therefore, the correct combination of people is **Tom and Sam**.