Question

the important rule for solving inequalities, that we dont worry about with equations is.....
○ if we divide or multiply by a negative, we use an open dot.
○ if we subtract or have negatives, we use a closed dot.
○ if we divide or multiply by a negative, we flip the symbol.
○ if we subtract or have negatives, we flip the symbol.
○ if we have parentheses, we need to distribute.

Explanation:

To solve this, we recall the key rule for inequalities vs equations. When solving equations, multiplying/dividing by a negative doesn't change the equality sign, but for inequalities, multiplying or dividing by a negative requires flipping the inequality symbol (e.g., from \(>\) to \(<\) or vice versa). Let's analyze each option:

• First option: Open dots relate to strict inequalities (not including the value), not multiplication/division by negative. Eliminate.
• Second option: Subtraction or negatives don't relate to closed dots (closed dots are for inclusive inequalities, like \(\geq\) or \(\leq\)). Eliminate.
• Third option: Matches the rule of flipping the symbol when multiplying/dividing by a negative in inequalities.
• Fourth option: Subtraction or having negatives doesn't require flipping the symbol. Eliminate. Also, distributing parentheses is done in both equations and inequalities, not a unique inequality rule.

Answer:

C. If we divide or multiply by a negative, we flip the symbol. (Assuming the third option is labeled C; if original labels were different, adjust, but the text of the correct option is "If we divide or multiply by a negative, we flip the symbol.")