Solve the following inequality and graph the solution: $$ (x-8)(x+3)0 $$ Choose test values and indicate whether the inequality is true or false in each region. Enter the test values from smallest to largest.

Question

Solve the following inequality and graph the solution: $$ (x-8)(x+3)>0 $$ Choose test values and indicate whether the inequality is true or false in each region. Enter the test values from smallest to largest.

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The solution to the inequality $$(x-8)(x+3)>0$$ is $$x \in (-\infty,-3) \cup (8,+\infty)$$. Test values: -4, 0, 9. Solve the equation $$ (x-8)(x+3)>0 $$. Solve the inequality by following steps: - step0: Solve the inequality by testing the values in the interval: $$\left(x-8 ight)\left(x+3 ight)>0$$ - step1: Rewrite the expression: $$\left(x-8 ight)\left(x+3 ight)=0$$ - step2: Separate into possible cases: $$\begin{align}&x-8=0\&x+3=0\end{align}$$ - step3: Solve the equation: $$\begin{align}&x=8\&x=-3\end{align}$$ - step4: Determine the test intervals: $$\begin{align}&x<-3\&-38\end{align}$$ - step5: Choose a value: $$\begin{align}&x_{1}=-4\&x_{2}=3\&x_{3}=9\end{align}$$ - step6: Test the chosen value: $$\begin{align}&x<-3 extrm{ } extrm{is the solution}\&-38 extrm{ } extrm{is the solution}\end{align}$$ - step7: The final solution is $$x \in \left(-\infty,-3 ight)\cup \left(8,+\infty ight):$$ $$x \in \left(-\infty,-3 ight)\cup \left(8,+\infty ight)$$ The solution to the inequality $$(x-8)(x+3)>0$$ is $$x \in (-\infty,-3) \cup (8,+\infty)$$. To graph the solution, we can choose test values in each region and determine whether the inequality is true or false in each region. Let's choose test values from smallest to largest: 1. Test value: -4 - $$(-4-8)(-4+3) = (-12)(-1) = 12 > 0$$ - The inequality is true in this region. 2. Test value: 0 - $$(0-8)(0+3) = (-8)(3) = -24 < 0$$ - The inequality is false in this region. 3. Test value: 9 - $$(9-8)(9+3) = (1)(12) = 12 > 0$$ - The inequality is true in this region. Therefore, the solution to the inequality $$(x-8)(x+3)>0$$ is $$x \in (-\infty,-3) \cup (8,+\infty)$$, and the test values are -4, 0, and 9.

Solve the following inequality and graph the solution: \[ (x-8)(x+3)>0 \] Choose test values and indicate whether the inequality is true or false in each region. Enter the test values from smallest to largest.

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Solve the following inequality and graph the solution: \[ (x-8)(x+3)>0 \] Choose test values and indicate whether the inequality is true or false in each region. Enter the test values from smallest to largest.

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