Question

SOLVE the following system of inequations

x2 - 6x + 5 greater than or equal to 0

x2 - 25 less than or equal to 0.

Answer 1

$$\begin{gathered} \left(\mathbf{1}\right) \\ {x}^2-6x+5\ge 0 \\ \Rightarrow x^2-5x-x+5\ge 0 \\ \Rightarrow x\left(x-5\right)-\left(x-5\right)\ge 0 \\ \Rightarrow \left(x-5\right)\left(x-1\right)\ge 0 \\ \mathbf{\Rightarrow }\mathit{x}\mathbf{\in }\mathbf{(}\mathbf{-}\mathbf{\infty }\mathbf{,}\mathbf{1}\mathbf{]}\mathbf{\cup }\mathbf{[}\mathbf{5}\mathbf{,}\mathbf{\infty }\mathbf{)} \\ \left(\mathbf{2}\right) \\ {x}^2-25\le 0 \\ \Rightarrow \left(x-5\right)\left(x+5\right)\le 0 \\ \Rightarrow \mathit{x}\mathbf{\in }\left[\mathbf{-}\mathbf{5}\mathbf{,}\mathbf{5}\right] \end{gathered}$$