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?
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.
-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.
This problem is from the textbook, but don't have explanation - only answer given
This problem is from the textbook, I copied problem directly from it (with different signs) but don't have explanation - only answer given
Yes, your reworked problem and solution are correct. When dividing by a variable, it is essential to consider the sign of the variable to maintain the inequality's direction.
Now, you have obtained two solutions for the given inequality:
1) x > -6
2) x < -20
To combine these two solutions and make the inequality signs the same, you can use the logical operators "AND" or "OR."
If you want to find the solution that satisfies both conditions simultaneously, you would use the logical operator "AND." The combined inequality solution would be:
x > -6 AND x < -20
But notice that there are no values of x that can simultaneously satisfy both conditions. This is because the two solutions are mutually exclusive (meaning they have no overlap) and cannot be true at the same time.
If you want to find the solution that satisfies either condition, you would use the logical operator "OR." The combined inequality solution would be:
x > -6 OR x < -20
In this case, any value of x that satisfies either condition (x > -6 or x < -20) will be a solution to the combined inequality.
Note: It's important to remember that in solving inequalities, the "AND" operator requires both conditions to be true, while the "OR" operator only requires at least one condition to be true.