Problems with Solving inequalities in matlab

Hello, I have a question on how to solve in matlab.

I have tried the following code:

syms x; 

f = (sqrt(x+1)-1)/x;
sol = solve(f<(sqrt(2)-1)/2,x);

but I only get the following error:

sol =
 
Empty sym: 0-by-1
 
Warning: Unable to find explicit solution. For options, see help. 

Is there someone out there who could help?

Answer 1

[John D'Errico]

That is not an error. It is a warning message, telling you there is a problem with what you have posed to solve.

There is no explicit solution found, because there are infinitely many solutions.

syms x; 
f = (sqrt(x+1)-1)/x;
fplot(f,[-5,100])
yline((sqrt(2)-1)/2);

A solution exists for ALL x, such that the curve is less than the horizontal line drawn. That is to say, whenever x strictly exceeds

xmin = solve(f == (sqrt(2)-1)/2)

xmin = 

vpa(xmin)

ans = 

13.65685424949237156668015607393

[Erik Börjesson]

Now I got it! Thank you very much!

[Matthew Cassini]

I don't get why it doesn't give the minimum or maximum value that is a solution, as that is normally how you would solve an inequality. If given 2x > 1 and asked to find x you would say x > 1/2, not theres infinitely many solutions.

[Torsten]

You get the "cut points" of your inequality if you solve it as an equation as John D'Errico did.

syms x
f = 2*x==1;
solve(f)

ans = 

Answer 2

[Walter Roberson]

solve() is pretty inconsistent as to whether it can handle inequalities. When it succeeds and you do not use returnconditions then it picks a representative solution instead of showing the inequality boundaries. For example if the range of solution was 3 to 15 it might say 9, but if it were -1 to 15 it might say 0