Assignments

In general, inequalities with fractions are difficult to solve. In order to solve such inequalities we use so-called 'number lines'.
It is very important to notice that it is very tricky to use cross-multiplication and it is highly discouraged to apply this popular technique with inequalities, see also Equations with fractions.

1. Solve:

$\displaystyle\frac{6}{x-4}>0$

2. Solve:

$\displaystyle\frac{2}{x^2+1}>0$

3. Solve:

$\displaystyle\frac{-5}{x^2+x+1}>0$

4. Solve:

$\displaystyle\frac{-3.2}{x+1}<0$

5. Solve:

$\displaystyle\frac{x}{x-3}>0$

6. Solve:

$\displaystyle\frac{x-1}{x+2}<0$

7. Solve:

$\displaystyle\frac{3}{x}<1$

8. Solve:

$\displaystyle\frac{2x}{x+2}>3$

9. Solve:

$\displaystyle\frac{x}{x^2-1}<0$

10. Solve:

$\displaystyle\frac{e^{x}-1}{e^{x}}>\displaystyle\frac{1}{e^{x}+1}$

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