Question

graph the solution to the following inequality on the num

$x^{2}-6x\leq -8$

note that you can use the aleks graphing calculator to

Explanation:

Step1: Rewrite the inequality

$$x^{2}-6x + 8\leqslant0$$

Step2: Factor the quadratic

$$(x - 2)(x - 4)\leqslant0$$

Step3: Find the critical points

Set $(x - 2)(x - 4)=0$, we get $x = 2$ and $x = 4$.

Step4: Test intervals

• For $x<2$ (e.g., $x = 0$), $(0 - 2)(0 - 4)=8>0$.
• For $2
• For $x>4$ (e.g., $x = 5$), $(5 - 2)(5 - 4)=3>0$.

Answer:

The solution is $2\leqslant x\leqslant4$. On the number - line, we draw a solid circle at $x = 2$ and $x = 4$ (because the inequality includes equality) and shade the region between them.