Why does the inequality sign change when both sides are multiplied or divided by a negative number? Does this?

Question

does this happen with equations? why or why not? write an inequality for your classmates to solve. in your inequality use the multiplication and addition properties of inequalities,

Answer 1

if a ≤ b then add " - b - a " to both sides......-b ≤ - a or - a ≥ - b



takes care of the equality question also

Answer 2

Why does the inequality sign exchange jointly as the two aspects are greater desirable or divided by using using a detrimental huge variety? via actuality by using using doing so which you're shifting the numbers from one component to the huge variety line's 0 component to distinctive. Take the inequality: 10 > a million as quickly as you multiply the two aspects of the inequality by using using -a million, can that throughout all danger make -10 greater effective than -a million? No, via undeniable fact which you're actual on the detrimental component to 0. you need to show the inequality sign via actuality -10 is under -a million, so which you write -10 < -a million. jointly as crossing 0 in the two direction, the inequality sign must be reversed.

Answer 3

Reversing the inequality symbol fixes the problem.

-why do wr reverse the sign when multiplying or dividing by a negative number?

Ex. -1<-5

if you multiply both sides by -1, you get 1<-5 which is false because a positive number cant be less than a negative one