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Nimfa-mama [501]
3 years ago
12

Help with this math question please

Mathematics
1 answer:
Marat540 [252]3 years ago
8 0
Re-arranging the inequality to find the test points:

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

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 \frac{(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)
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