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^2-4x=21 ⇔ 1x^2+( - 4)x+( - 21)=0We see above that a= 1, b= - 4, and c= - 21. 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=4± 10/2
x=4+ 10/2
x=4- 10/2
x=4/2 + 10/2
x=4/2 - 10/2
x=7
x=- 3
Step 2
The solutions of the related equation are - 3 and 7. 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 ≤ - 3. For simplicity, we will choose x=- 4.
