Posted by **Anonymous** on Sunday, January 13, 2008 at 10:12pm.

How would you solve the following inequality algebraically?

0.5(x + 2)^2 (x - 4) > 2x + 3

- How would you solve the following inequality -
**Damon**, Monday, January 14, 2008 at 10:59am
I would graph it to get close and look for intersections numerically.

You know that the cubic at left hits the x axis three times, grazes at x = -2 and crosses at x = 4

it starts at the lower left, y is big negative if x is big negative

then it bounces off the x axis at x = -2 and drips down to cross the y axis at y = -8 then goes up through x = 4 to x big + x and big +y on the right

the straight line on the right goes through (0,3) and (-3/2,0)

The curve crosses the line somewhere between x - -2and x = 0

You can see that the curve is above the line at the lower left but may cross for large negative x and it dips below at the lower right but might come up and cross agin for large + x

I would have to search for those crossings numerically.

- How would you solve the following inequality -
**Damon**, Monday, January 14, 2008 at 11:19am
ps

Once you have one root numerically, you can factor that out and be left with a quadratic.

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