This week in Pre-Calc, I struggled with understanding how to solve quadratic inequalities, so here is how to do them.
First, you factor the equation. Next, you take the two numbers that will be used to factor and write them in two separate brackets next to “x”. Next, you take the first number from the original equation, and use that as the bottom number of a fraction of each number next to “x” in each bracket. After, you simplify the fractions, and if the number is still in fraction form, then you take the bottom number and put it in front of the “x” in the bracket, because you cannot have it in fraction form. Next you take the numbers next to “x” and give them the opposite sign that they originally had (positive or negative) and then you use those numbers, however if one or both of the numbers was a fraction, then you would put it back into it’s simplified (if possible) fraction form, and still reverse the original sign that it had, as you did with the other number. After, you put both numbers on a number line. You would use a closed circle if it is not = to zero (greater or lesser), or an open circle if it is = to zero (greater or lesser). Once both numbers are placed on the number line, you choose one number in each section (left, middle and right) of the numbers, and test them by plugging them into the equation that you created, and then you are able to determine which sections work with the equation, and therefore determine which numbers are greater, lesser or equal to “x”.