Now, we can find the critical points by setting the expression equal to zero: (2x + 1)(x + 1) = 0 This gives us two critical points: x = -1 (from x + 1 = 0) x = -1/2 (from 2x + 1 = 0)
Next, we can plot these critical points on a number line and test a point in each interval to determine whether the expression is positive or negative. This will give us the solution to the inequality.
Testing x = -2: 2(-2)^2 + 3(-2) + 1 = 8 - 6 + 1 = 3, which is positive.
Therefore, the solution to the inequality 2x^2 + 3x + 1 ≥ 0 is x ≤ -1 or x ≥ -1/2.
To solve this inequality, we can use the method of factoring and graphing.
First, let's factor the quadratic expression:
2x^2 + 3x + 1 = (2x + 1)(x + 1)
Now, we can find the critical points by setting the expression equal to zero:
(2x + 1)(x + 1) = 0
This gives us two critical points:
x = -1 (from x + 1 = 0)
x = -1/2 (from 2x + 1 = 0)
Next, we can plot these critical points on a number line and test a point in each interval to determine whether the expression is positive or negative. This will give us the solution to the inequality.
Testing x = -2:
2(-2)^2 + 3(-2) + 1 = 8 - 6 + 1 = 3, which is positive.
Therefore, the solution to the inequality 2x^2 + 3x + 1 ≥ 0 is x ≤ -1 or x ≥ -1/2.