Flashcard 17 - Mathematics: Quantitative Reasoning Flashcard Set for the TSIA2

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When manipulating algebraic equations, we can add, subtract, multiply, or divide both sides of an equation by any number (except \(0\)) and the equation will still hold true. This is true for inequalities as well, but with one exception. When multiplying or dividing an inequality by a negative number, we reverse the inequality sign. An example is shown below:

\[-2y > 10\] \[\dfrac{-2y}{-2} > \frac{10}{-2}\] \[y < -5\]

Note that we reversed the \(>\) sign to the \(<\) sign when we divided by \(-2\) (a negative number).