Use interval notation to write the solution sel of the inequality

The solution set is .
(Type your answer in interval notation.)

Ask by Mcguire Simpson. in the United States

Jan 21,2025

Question

Use interval notation to write the solution sel of the inequality $$ x^{2}+5 x-14 \leq 0 $$ The solution set is $$ \square $$. (Type your answer in interval notation.)

UpStudy AI · Accepted Answer

Solve the equation $$ x^{2}+5x-14=0 $$.
Solve the quadratic equation by following steps:
- step0: Solve by factoring:
  $$x^{2}+5x-14=0$$
- step1: Factor the expression:
  $$\left(x-2ight)\left(x+7ight)=0$$
- step2: Separate into possible cases:
  $$\begin{align}&x-2=0\&x+7=0\end{align}$$
- step3: Solve the equation:
  $$\begin{align}&x=2\&x=-7\end{align}$$
- step4: Rewrite:
  $$x_{1}=-7,x_{2}=2$$
The solutions to the equation $$x^{2}+5x-14=0$$ are $$x=-7$$ and $$x=2$$.

Now, we need to find the solution set of the inequality $$x^{2}+5x-14 \leq 0$$. To do this, we can use the solutions we found earlier to determine the intervals where the inequality is true.

The inequality $$x^{2}+5x-14 \leq 0$$ is true when $$x$$ is between the solutions $$x=-7$$ and $$x=2$$. Therefore, the solution set in interval notation is $$[-7, 2]$$.
The solution set is $$[-7, 2]$$.

Use interval notation to write the solution sel of the inequality

The solution set is .
(Type your answer in interval notation.)

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Use interval notation to write the solution sel of the inequality The solution set is . (Type your answer in interval notation.)