Test a value from each interval to see if it satisfies the original inequality.
Step 1
We will start by solving the related equation.
11 = 4x^2+7x ⇔ - 4x^2+( - 7)x+ 11=0We see above that a= - 4, b= - 7, and c= 11. 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 ± 15/- 8
x=7 + 15/- 8
x=7 -15/- 8
x=- 7/8-15/8
x=- 7/8+15/8
x=- 2.75
x=1
Step 2
The solutions of the related equation are - 2.75 and 1. 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 ≤ - 2.75. We will choose x=- 4.
