Question

solve the nonlinear inequality. express the solution using interval notation.
x^2 + 3x > 28
graph the solution set.
use the tools to enter your answer.

Explanation:

Step1: Rearrange the inequality

Move 28 to the left - hand side: $x^{2}+3x - 28>0$.

Step2: Factor the quadratic expression

Factor $x^{2}+3x - 28$ as $(x + 7)(x - 4)>0$.

Step3: Find the roots

Set $(x + 7)(x - 4)=0$. The roots are $x=-7$ and $x = 4$.

Step4: Test the intervals

We have three intervals to test: $(-\infty,-7)$, $(-7,4)$ and $(4,\infty)$.
For $x<-7$, let $x=-8$. Then $(-8 + 7)(-8 - 4)=(-1)\times(-12)=12>0$.
For $-7For $x>4$, let $x = 5$. Then $(5 + 7)(5 - 4)=12\times1 = 12>0$.

Answer:

The solution in interval notation is $(-\infty,-7)\cup(4,\infty)$.
To graph the solution set on the number - line:

• Place open circles at $x=-7$ and $x = 4$ (since the inequality is $>$ and not $\geq$).
• Shade the regions to the left of $x=-7$ and to the right of $x = 4$.