Question

question 12 solve the following inequality and graph the solution: (x - 6)(x + 3) ≤ 0 and draw the solution -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 clear all draw:

Explanation:

Step1: Find the roots

Set $(x - 6)(x + 3)=0$. Then $x-6 = 0$ gives $x = 6$ and $x+3=0$ gives $x=-3$.

Step2: Test intervals

Consider the intervals $x < - 3$, $-36$.
For $x < - 3$, let $x=-4$, then $(-4 - 6)(-4 + 3)=(-10)\times(-1)=10>0$.
For $-3For $x>6$, let $x = 7$, then $(7 - 6)(7 + 3)=1\times10 = 10>0$.

Step3: Determine solution

The inequality $(x - 6)(x + 3)\leq0$ is satisfied when $-3\leq x\leq6$.

Answer:

The solution of the inequality is $-3\leq x\leq6$. On the number - line, we use a closed - circle at $x=-3$ and $x = 6$ and draw a line segment between them.