Question

x/(x-4)>5

Answer 1

what are you looking for

Answer 2

solve the polynomial inequality

Answer 3

I'd multiply by the square of the denominator

\[\frac{x}{(x -4)} \times (x - 4)^2 > 5 (x - 4)^2\]

which becomes

\[x(x-4) - 5(x - 4)^2 > 0\]

so look at simplifying and you get

\[(x -4)(x - 5(x -4))> 0 ...or ....(x - 4)(-4x + 20) > 0\]

so the critical values are x = 4 and x = 5

so the number line is divided into 3 parts



now write the inequality that matches the solution shown...