inequalities help?

Question

ok, -4<2-x<6
so u subtract 2 from all sides and that leaves u with -6<-x<4, so u have to get rid of the negeative in front of x, so u divide all sides, so i got: 6

i know ur supposed to flip the sign, but how would u solve it?

Answer 1

When you multiply (or divide) an inequality by a negative number, you have to reverse the direction of the inequality.

Another way to approach it is to write the problem as two separate inequalities, simplify then rewrite it.

-4 < 2 - x < 6

-4 < 2 - x and 2 - x < 6

-4 < 2 - x
0 < 6 - x add 4 to both sides
x < 6 subtract x from both sides

2 - x < 6
-4 -x < 0 subtract 6 from each side

-4 < x add x to each side

- 4 < x < 6 restate the two inequalties

Answer 2

Ok. Here is what I would do for this problem:
Take apart the inequality. say -4<2-x and 2-x<6

-4<2-x 2-x<6
-2 -2 -2 -2

-6<-x -x<4
(divide each side by -1--when you divide by a negative number you have to switch the sign)

6>x and x>-4

2nd way to do the problem

subtract the 2 from each side
you get: -6<-x<4
then divide each side by -1 and flip the signs
you get 6>x>4 ( same answer as before.

Answer 3

When you divide by a negative number the equality signs change direction so you should have 6>x>-4

Answer 4

-4<2-x<6 can also be stated as two different equations.
It is easier to solve that way.
2-x>-4 and 2-x<6.
Take each problem one at a time and then combine them.
2-x>-4
2>x-4
4>x This can be written as x<4.

2-x<6
2 -4
Now, you combine.
-4 x<4
-4 This is read as x is greater than negative 4 and less than 4.

Answer 5

When dividing/multiplying inequalities by a negative number, you must flip the inequality sign. Consider you have:
a < b
this is the same as
b - a > 0
if we multiply by -1, we must switch the inequality, since the left side is now negative. so:
a - b < 0
-b < -a

Another way to see it is to take what you start with and switch which side of the inequality they are on:
a < b
subtract b from both sides
a-b < 0
add -a to both sides
-b < -a

Answer 6

When you divide or multiply inequalities by a negative the signs change. So if you had -x>4, then when you divided by the negative 1, you'd have x<-4.

Answer 7

If i remember correctly, you need to switch the signs when dividing by a negative. This would leave you with 6>x>-4, which is true.

Answer 8

to get rid of the negative in front of x u have to multiply with -1 and as far as i can remember from my high-school time the direction of the inequality changes and we have:
6> x> -4
hope i could help!

Answer 9

Break it into two

-4<2-x

So, -4-2<-x
or -6<-x

So, 6>x , multiplying or dividing by -1 changes the inequality

Similarly, 2-x<6

or -x<6-2
or -x<4
or x>-4

Combining them you have

6>x>-4

or -4
Perfectly fine

Answer 10

ok as long as you know what your doing you just want to get the variable by itself, x.. and then multiply by the reciprical once you get the variable and one number by itself. now if you multiply by two on the reciprical you switch the signs it wouldnt be < anymore it would be >. BUT THATS ONLY IF YOU MULTIPLY A NEGATIVE WHEN YOU DO THE RECIPRICAL.