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=5 ⇔ - 3x^2+ 10x+( - 5)=0We see above that a= - 3, b= 10, and c= - 5. 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(40)/- 6
x=- 10 + sqrt(40)/- 6
x=- 10 - sqrt(40)/- 6
x=- 10/- 6+sqrt(40)/- 6
x=- 10/- 6-sqrt(40)/- 6
x=10/6-sqrt(40)/6
x=10/6+sqrt(40)/6
x≈ 0.61
x≈ 2.72
Step 2
The solutions of the related equation are approximately 0.61 and 2.72. 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 < 0.61. For simplicity, we will choose x=0.
