Verified answer

This is a little easier because one side of the inequality is zero.

The expression on the left will be zero when any of its factors is zero. So, the left will be zero when x = 1/2, -4, and 3.

These three x-values separate the number line into four pieces: the numbers less than -4, the numbers between -4 and 1/2, the numbers between 1/2 and 3 and the numbers larger than 3. Pick a test value from each of the regions to see if the result is larger than zero. If that test value makes the inequality true, then so does every number from that same region.

For example, -5 is less than -4. If I put -5 in for x, (-11)(-1)(-8)^2 which ends up being 704. Definitely larger than zero. So the values less than -4 are solutions.

0 is between -4 and 1/2. Putting in 0 gives me (-1)(4)(-3)^2 = -36. Less than zero. The values between -4 and 1/2 are NOT solutions.

1 is between 1/2 and 3. x = 1 gives (1)(5)(-2)^2 = 20. Larger than zero. The values between 1/2 and 3 are solutions.

4 is larger than 3. x = 4 gives (7)(11)(4)^2 which is definitely larger than zero.

So the solution is all x values except the numbers between -4 and 1/2.

Another way to do this type of problem is to graph the equation y = (2x-1)(x+4)(x-3)^2 using a graphing calculator. Since we want the value of the expression on the right of this equation to be greater than or equal to zero, we look for the parts of the graph that are above the x-axis plus each x-intercept.

What is (2x-1)(x+4)(x-3)^2 ≥ 0?

For (2x-1)(x+4)(x-3)^2 to be ≥ 0, the following should be true:

(1) 2x-1 ≥ 0

(2) x+4 ≥ 0

(3) (x-3)^2 ≥ 0

From (1):

2x-1 ≥ 0

2x ≥ 1

x ≥ 1/2

From (2):

x+4 ≥ 0

x ≥ -4

From (3):

(x-3)^2 ≥ 0

x-3 ≥ 0

x ≥ 3

(2x-1)(x+4)(x-3)^2 ≥ 0

substitute 0 for x

(2*0-1)(0+4)(0-3)^2≥0

(-1)(4)(-3)^2≥0

(-1*4)(-3)^2≥0

(-4)(-3)^2≥0

7^2≥0

I hope that helps, and that it's right, sorry if it's not, it's been awhile since i've done one of these problems!

the spots where it equals zero are 1/2, -4, 3

tests points on all sides of these values to find what works

x is less than -4 or x is greater than 1/2

im sry i cant- not good at math

PLEASE answer mine at http://answers.yahoo.com/question/index?qid=200807... (not emergency but need the help!!)

thank you for ur help!