Test a value from each interval to see if it satisfies the original inequality.
Step 1
We will start by solving the related equation.
- 3x^2-10x=- 1 ⇔ - 3x^2+( - 10)x+ 1=0We see above that a= - 3, b= - 10, and c= 1. 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=10±sqrt(112)/- 6
x=10 + sqrt(112)/- 6
x=10 - sqrt(112)/- 6
x=- 5/3-2sqrt(7)/3
x=- 5/3+2sqrt(7)/3
x≈ - 3.43
x≈ 0.097
Step 2
The solutions of the related equation are approximately - 3.43 and 0.097. 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 < - 3.43. For simplicity, we will choose x=- 4.
