Question

Suppose you are solving an inequality. Under what circumstances do you reverse the inequality symbol? Select all that apply.A. adding a negative number on both sidesadding a negative number on both sidesB. subtracting a negative number on both sidessubtracting a negative number on both sidesC. multiplying by a negative number on both sidesmultiplying by a negative number on both sidesD. dividing by a negative number on both sides

Answer 1

Answer:

The correct options are C and D

Only multiplication by a negative number and division by a negative number changes the inequality sign

Explanation:

Consider the inequality:

$5>2$

This is clearly true that 5 is greater than 2

adding a positive number on both sides would not change the inequality sign, because:

$\begin{gathered} 5+1>2+1 \\ 6>3 \end{gathered}$

6 is truly greater than 3

Same thing goes with subtracting a negative number, it won't change the inequality sign.

Multiplying by a negative number though,

$\begin{gathered} 5\times-2>2\times-2 \\ -10>-4 \end{gathered}$

This is NOT TRUE, because -10 is less than -4, and hence, we change the inequality sign as

$-10$

Division by a negative number also changes the inequality sign.

In conclusion, only multtplication by a negative number and division by a negative number changes the inequality sign.