Question

1. solve and graph the inequality x² + 9x - 90 < 0. change inequality to equal and factor. same factors of 90. solve for x. graph answers on number line. check - numbers in each region. solution and

Explanation:

Step1: Convert to equation and factor

Set $x^{2}+9x - 90=0$. Factor the quadratic equation: $x^{2}+9x - 90=(x + 15)(x-6)=0$.

Step2: Solve for x

Set each factor equal to zero: $x+15 = 0$ gives $x=-15$; $x - 6=0$ gives $x = 6$.

Step3: Test intervals

The intervals to test are $x<-15$, $-156$. For $x<-15$, let $x=-16$, then $(-16 + 15)(-16 - 6)=(-1)\times(-22)=22>0$. For $-156$, let $x=7$, then $(7 + 15)(7 - 6)=22\times1=22>0$.

Answer:

The solution of the inequality $x^{2}+9x - 90<0$ is $-15