inequalities

inequalities

1. you solve an inequality like a regular equation, EXCEPT if you are multiplying or dividing by a negative number

   • if you need to multiply or divide by a negative number you must flip the inequality sign
     • EXAMPLE
       • solve 9 - 2x > 15
         • -9
           • -2x > 6
             • ÷ -2
               • x < -3
                 • the sign switches because you divided by a negative number

2. inequalities on a number line

   • main thing is that if it is </> then it is a circle but if it is ≤/≥ then it is represented with a filled in dot

3. one rule with quadratic inequalities:

   • if x² > a² then x > a or x < -a
     • if x² < a² then -a < x < a
   • example
     • solve the inequality x² ≤ 25
       • x = ± 5
         • -5 ≤ x ≤ 5

4. you can use the quadratic graph to help solve a quadratic inequality

   • first make the quadratic equal to 0 and then factorise. then solve the equation to see where it crosses the x axis
     • if your quadratic is > 0 then you're focusing on the section of the graph above the x axis and vice versa.
       • then you can see on the graph which inequality signs to use for your solutions for x. If the part of the graph that you're focusing on inculdes the turning point, then it will be a < x < b, but if the part of the graph is just 2 of the lines are seperate it will be x < a and x > b

5. to show inequalities on a graph, change them into an equation plot it on the graph using a solid line if the inequality is ≤/≥ and a dotted line if its </>, then work out which side of the line you want by substituting in coordinates and seeing if the inequality is correct then that is the region that satisfies the inequality

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