TABLE OF CONTENTS
Solve the inequality 3x2 – 8x + 4 > 0.
The first step of solving an inequality is to find the roots.
(3x – 2)(x – 2) > 0
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The roots are and x = 2.
Putting the roots on the number line and evaluating each regions shows us that the equation is positive when and 2 < x < ∞.
Solve the inequality -x2 – 4x > 3.
If things have to be unequal, they may as well be unequal for everyone.
x2 + 5x + 3 < 0
So start off by putting everything on the same side of the inequality.
The next step is to put on some gloves, find a tree, bush, shrub, or other plant, and look for roots. The quadratic formula can be a big help in this.
These are about x = -0.7 and x = -4.3.
The number line shows that the equation is negative from -4.3 < x < -0.7. Maybe if it had a lollypop it would feel better?
Solve the inequality -2x2 + 8x + 8 ≤ 0.
Be careful here.
x2 – 4x – 4 ≥ 0
You want to get rid of the -2 from the equation, but you have to reverse the inequality when you do.
Now we search for the roots.
These are about x = -0.8 and x = 4.8.
So our negative values are from -∞ < x < -0.8 and 4.8 < x < ∞
We tell it to you straight.
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