Question

Help with this math question please

Answer 1

Re-arranging the inequality to find the test points:


`x- (70)/(x)\ \textless \ -3 \\ \\ x- (70)/(x)+3\ \textless \ 0 \\ \\ ( x^(2) -70+3x)/(x)\ \textless \ 0 \\ \\ ((x-7)(x+10))/(x)\ \textless \ 0`

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
`((x-7)(x+10))/(x)` 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)