Solving Inequalities With Algebra

1. Rearrange the inequality so right side is 0. Remember Negative Flip. Don’t try to move terms including variables through sides(you dont know if they are negative or positive)
2. Find Critical Values of the polynomial
3. Draw a number line or Chart
4. Pick tests for you number line or chart to find positive or negative values. THINK BIG

Example with DOS

$(4-x^2)(x^2-3x+2)\le 0$ $(2+x)(2-x)(x-2)(x-1)\le 0$ Notice that $(2-x)$ and $(x-2)$ are very close. $(-x+2)(x-2)=-(x-2)(x-2)=-(x-2{)}^2$ $(-)(2+x)(x-2{)}^2(x-1)\le 0$ Now get the x intercepts: they are: {-2(order 1),2(order 2),1(order 1)} The chart:

Test	x < -2	x = -2	-2 < x < 1	x = 1	1 < x < 2	x = 2	x > 2
-(x+2)(x-2)^2(x-1)	-	0	+	0	-	0	-
Less or equal to zero intervals are: x ≤ -1 ∪ x ≥ 1