At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
I don't know who would actually solve it in a way that would intentionally make negative numbers.
Well to solve any equation you would first add or subtract the solitary number that's on the same side as the variable (x in this case) to get x on it's own. Then divide or multiply both sides by the number attached to the variable.
Oh, I skipped a part I just realized. You would first need to get all your vairables together on one side of the equation.
If it were up to me, I would add 3x to both sides and add 14 to both sides to get 5x > 10 x > 2 but even if it were -1o > -5x I would still add 5x and add 10 to both sides to get 5x > 10 The point is, you don't have to end up dividing by a negative number to get the solution.
Also note: When you divide or multiply both sides of an inequality by a negative, your inequality flips. So < becomes > and > becomes <
PsychoTink, that's the exact point I was trying to discourage people from doing because it leads to confusion.
just swap the sides of the -5x and -10 to make them both positive without having to divide by negative numbers
I would have also Hero, I would have kept things positive, but this one we'd have to blame on whomever wrote the book or problem the person is asking about. It looks like a multiple choice question to find the missing bit, and the book decided to be weird and make it really difficult.
No, what I'm saying is, even if you get to -1o > -5x The next step is to add 5x to both sides, then add 10 to both sides all in one step to get 5x > 10
You can actually just swap the sides immediately when you see a negative on the variable.
For example if -2x > 4, immediately swap sides to get -4 > 2x
If you do it that way, you'll never have to worry about dividing inequalities by negative numbers.
You could, but that's the really hard way to do it. Why would you have even put the x on that side. You can see that it starts negative, and you're only going to make it more negative by subtracting the 2, instead you could add the 3 right off the top and never have a negative situation
It's not the hard way if you think about it. I did it in one single step. You just swap the sides -2x > 4 -4 >2x -2 > x How is that the hard way?
Well, if you have to show all your work it would be the hard way when you could have avoided it from every happening.
|dw:1327690510831:dw| Dividing by negatives then remembering to switch the signs is the reason why students get things wrong. The point is to get the answer correct.
Who cares if you have to show all your work. If you do it that way, you'd never have to worry about getting it wrong because you "forgot to switch a sign after dividing by a negative".
By the way, the answer to the original question is -14 > -4 - 5x
I completely agree with you Hero, that's why I was saying to take notice of what it's going to do in the start when you first have to combine your x. Right there you can see if you'll have a negative x or not and can start the problem accordingly. Rather than having to put yourself in that situation later.
Sometimes though, you can't avoid getting negatives. In that case, you can use my method.
I guess that's true.