Test a value from each interval to see if it satisfies the original inequality.
Step 1
We will start by solving the related equation.
4x^2-19x=- 12
⇕
4x^2+( - 19)x+ 12=0We see above that a= 4, b= - 19, and c= 12. 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 = 19 ± 13/8
x = 19 + 13/8
x = 19 - 13/8
x = 32/8
x = 6/8
x = 4
x = 0.75
Step 2
The solutions of the related equation are 4 and 0.75. 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 ≤ 0.75. For simplicity, we will choose x=- 1.
