Question

Reiny, the problem with the answer x>-2, why divide by 1? Is it because you can't divide with variable?

Reworked problem

-7x>-2(x+15)<10
-7x>-2(x+15)
-7x + 2x > 30
-5x/-5 > 30/-5
x > -6

other side
-2(x+15)<10
-2x-30<10
-2x-30+30<10+30
-2x/-2 < 40/-2
x < -20

Is this correct and how do I combine the two answers and make inequality/equality sign the same?

Answer 1

for your first question, you must be referring to
http://www.jiskha.com/display.cgi?id=1449763017

from the point
-x < 2 , or -1x < 2

remember to get x "alone" you divide by the coefficient of x, in this case -1
and of course since we divided by a negative, the inequality sign has to be reversed, I think you knew that
so
-x < 2
-x/-1 > 2/-1
x > 2

for the second one....
http://www.jiskha.com/display.cgi?id=1449762096

I had objected to the fact that for the compound inequality your inequality signs don't go in the same direction
If we place AND between your two solutions
we have
x < -20 AND x > -6
this is not possible, (show it on a number line)

if we place OR between your two solutions
we have
x < -20 OR x > -5 , which is a solution
BUT we cannot write it as a compound statement and we MUST write it as
x < -20 OR x > -5

As I said in the other post, using a compound statement with the inequality signs going the same way, means we have the connective AND

Is this from a textbooK?
If so, then the question is flawed.

Answer 2

-7x>-2(x+15)<10
are you sure this is not a typo?
Usually arrows would be the same direction

certain error:
-7x>-2(x+15)
IS NOT
-7x + 2x > 30
but
-7x + 2 x > -30
what happened to the - sign?

-5x/-5 > 30/-5
x > -6
NO - if you multiply both sides of an inequality by a negative, you REVERSE the arrow direction.

I suspect your very first line is wrong so am not going to put more time into this.

Answer 3

This problem is from the textbook, but don't have explanation - only answer given

Answer 4

This problem is from the textbook, I copied problem directly from it (with different signs) but don't have explanation - only answer given