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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

Suppose you are solving an inequality. Under what circumstances do you reverse the-example-1
User Runtime Terror
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20 votes

Answer:

The correct options are C and D

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

Step-by-step 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*-2>2*-2 \\ -10>-4 \end{gathered}

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


-10<-4

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.

User KCGD
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