Question

Create a rational inequality whose solution is$(-\infty ,-2]\cup [4,\infty ).$

Short answer

Solution to the rational function is$(\mathrm{x}+2)(\mathrm{x}-4)\ge 0.$

Step-by-step solution

Step 1. Given data

Given that the rational function is$(-\infty ,-2]\cup [4,\infty ).$

Step 2. Rational function

Take x as variable and R(x) be the rational function as $\mathrm{x}\in (-\infty ,-2]\cup [4,\infty ).$It is indicated by closed inequality and R(x) must have numerator.

$\mathrm{R}\left(\mathrm{x}\right)=(\mathrm{x}+2)(\mathrm{x}-4)$

Step 3. Number line

It can be indicated as,

Step 4. Rational inequality

The rational inequality should be$\mathbf{(}\mathbf{x}\mathbf{+}\mathbf{2}\mathbf{)}\mathbf{(}\mathbf{x}\mathbf{-}\mathbf{4}\mathbf{)}\mathbf{\ge }\mathbf{0}\mathbf{.}$