-11<4x-3<9 help?

Question

help what is the solution set?

Answer 1

-11<4x-3<9 ... Add 3 to each and
-8 < 4x < 12 ... Divide each by 4 and
-2 < x < 3

Answer 2

If - 11 < 4x - 3 < 9 , then (adding 3 to all)

- 11 + 3 < 4x < 9+3 which is to say - 8 < 4x < 12

And, if that's true, then (dividing all by 4) - 2 < x < 3

So x has to be bigger than - 2 and smaller than 3. Like 0 is a number that satisfies that original statement. Try plugging it in and see for yourself:

- 11 < 4 (0) - 3 < 9

- 11 < - 3 < 9 which is true!

Then try some other numbers in that range and see that they all make that original statement true.


Now try plugging in some numbers not in that range, like - 3 or 5 and see that they make the statement false.

And, notice that the numbers on the edge, - 2 and 3 also make the statement false, as there is no equality in those less-than signs.

Depending on how you're supposed to write your answer, the solution set is:

- 2 < x < 3

or ( - 2 , 3 )

Answer 3

-11<4x-3<9
-11 + 3 < 4x - 3 + 3 < 9 + 3
-8 < 4x < 12
divide everything by 4, to solve for x...
-2 < x < 3 is the solution set...or

{x|-2 < x < 3} in set-builder notation; and
(-2,3) in interval notation

Answer 4

solve the two inequality seperately

-11< 4dx-3
-8< 4x
-2 < x

and 4x -3 < 9
4x < 12
x < 3

combine the result
-2