Test a value from each interval to see if it satisfies the original inequality.
Step 1
We will start by solving the related equation.
1x^2+ 6x+( - 16)=0We see above that a= 1, b= 6, and c= - 16. Let's substitute these values into the Quadratic Formula to solve the equation.
Now we can calculate the first root using the positive sign and the second root using the negative sign.
x=- 6 ± 10/2
x=- 6 + 10/2
x=- 6 - 10/2
x=- 6/2 + 10/2
x=- 6/2 - 10/2
x=2
x=- 8
Step 2
The solutions of the related equation are - 8 and 2. Let's plot them on a number line. Since the original is a strict inequality, the points will be open.
Step 3
Finally, we must test a value from each interval to see if it satisfies the original inequality. Let's choose a value from the first interval, x < - 8. For simplicity, we will choose x=- 10.
