What happens when dividing by a negative in an inequality?

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In summary, the conversation discusses the process of rearranging and solving inequalities, with a focus on dividing by negative numbers and the resulting change in the direction of the inequality symbol. The most efficient method is debated, with some preferring to read left to right while others prefer to read right to left.
  • #1
Yazan975
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  • #2
-10 < 2x + 3 < -1
-13 < 2x < -4
-13/2 < x < -2
 
  • #3
-c < ax + b < -d

Easier to work with (after re-arranging):
c > -(ax + b) > d
 
  • #4
Wilmer said:
-c < ax + b < -d

Easier to work with (after re-arranging):
c > -(ax + b) > d
But when you get to the step c + b > -ax > d + b you have to divide by -a anyway and the >s flip again. I think it's good in that you get that extra step (to stress the point of what happens when you divide by a negative) but greg1313's method is slightly more efficient.

-Dan
 
  • #5
topsquark said:
But when you get to the step c + b > -ax > d + b you have to divide by -a anyway and the >s flip again. I think it's good in that you get that extra step (to stress the point of what happens when you divide by a negative) but greg1313's method is slightly more efficient.
-Dan
Ya...agree...BUT li'l ole me prefers ? > ? > ? to ? < ? < ?
A bit like reading left to right instead of backwards!
Anyway, not important...
 

Related to What happens when dividing by a negative in an inequality?

What is the possible range of values?

The possible range of values refers to the minimum and maximum values that a particular variable can take on. It is the entire spectrum of values that are theoretically possible for that variable.

Why is knowing the possible range of values important?

Knowing the possible range of values is important for understanding the limitations and potential of a particular variable. It can also help in making predictions and setting realistic expectations.

How is the possible range of values determined?

The possible range of values can be determined through experimentation, statistical analysis, or theoretical calculations. It depends on the specific variable and the available data or information.

Can the possible range of values change?

Yes, the possible range of values can change depending on various factors such as new discoveries, changes in technology, or shifts in the environment. It is important to regularly reassess the possible range of values for accurate and up-to-date information.

Are there any limitations to the possible range of values?

There may be limitations to the possible range of values, especially in situations where there is incomplete or insufficient data. It is also possible that the true range of values may be outside of the currently known or calculated range. Therefore, the possible range of values should always be viewed as a rough estimate rather than an absolute truth.

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