Test a value from each interval to see if it satisfies the original inequality.
Step 1
We will start by solving the related equation.
x^2+7x=- 10 ⇔ 1x^2+ 7x+ 10=0We see above that a= 1, b= 7, and c= 10. 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=- 7 ± 3/2
x=- 7 + 3/2
x=- 7 - 3/2
x=- 7/2+3/2
x=- 7/2-3/2
x= - 2
x= - 5
Step 2
The solutions of the related equation are - 2 and - 5. Let's plot them on a number line. Since the original is not a strict inequality, the points will be closed.
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 ≤ - 5. For simplicity, we will choose x=- 10.
