Question

3<5-2x<7 How To Solve This?

Answer 1

2x can only be 0 in this case.
x = 0

Answer 2

Noo Betwen 3 and 7 it needs Just X Not 0

Answer 3

You can try and solve it by substituting the values.

Answer 4

a Ok Thanks a lot

Answer 5

If x=1/2, then the inequality holds... So x=0 isn't the only answer.

Answer 6

There are some axioms from real analysis that you can use on inequalities like this. Firstly, I would break up the inequality into two so that it's a little easier to work with. This will give you two regions of solutions for x, and the overlap of solutions is where the solutions work for both halves, and therefore are the solutions to the whole thing.

3<5-2x<7. Break up into 3<5-2x and 5-2x<7. Use some axioms to work on this (you can add any real number to both sides without changing the inequality, and you can multiply both sides by a positive real number and not change the inequality. If you need to multiply by a negative number, then the inequality sign changes. All of these rules come from the area of maths called real analysis).

When you do the above, you get 1>x and x>-1. The intersection of these two regions is -1<x<1. If there were no numbers in this intersection, then it would mean there are no solutions, since to satisfy the left inequality you can only use some values of x, but to satisfy the right inequality then you need different values of x, and therefore you can't find any that satisfy both. However there are values which satisfy both: -1<x<1.