Re-arranging the inequality to find the test points:
[tex]x- \frac{70}{x}\ \textless \ -3 \\ \\
x- \frac{70}{x}+3\ \textless \ 0 \\ \\
\frac{ x^{2} -70+3x}{x}\ \textless \ 0 \\ \\
\frac{(x-7)(x+10)}{x}\ \textless \ 0 [/tex]
This means, we need to test the inequality for x = -10, x = 0 and x = 7
Since question assumes that x > 0, so we ignore the values less than 0.
So the test points are x = 0 and x = 7
At x = 0 the expression is undefined.
Between x = 0 and x = 7 the value of expression [tex] \frac{(x-7)(x+10)}{x}[/tex] is negative. At x = 7 the value of expression is 0. Above x = 7 the value of expression is positive.
So, the solution to the given inequality will be 0 < x < 7.
In Interval notation, the solution can be written as (0,7)
