Inequalities | O Level Mathematics 4024 & IGCSE Mathematics 0580 | Detailed Free Notes To Score An A Star (A*)

Inequalities

• The question will always ask you to tell the inequalities that cover the shaded or unshaded region.
  • Remember, read carefully if it is asking for the shaded region or the unshaded region
• If they don’t give you ANY inequality and you have to find all of them
  • Then
    • It will always be if the line is NOT DOTTED
    • It will always be if the line is dotted
  • If however
    • He gives an inequality where dotted line is denoted as or a non dotted line is shown as
      • Then you do yours as he does
    • MOST CASES
      • The first one applies that is mentioned above
        • It will always be if the line is NOT DOTTED
        • It will always be if the line is dotted
      • A vertical line
        • Will always be denoted with x is either greater than or lesser than (or greater than equal to or lesser than equal to) something
          • See the number on the graph where the line cuts x
          • Then, just consider it as x is related to that number
        • For example
          • We have a NOT DOTTED line that cuts the x axis at 5
          • Then the equation of the line is x=5
        • However now we need to consider which side will be greater to and which side will be lesser to
        • If you are finding the inequality for the shaded region
          • Then
            • The left side of the line will be ( if the line was dotted)
            • The right side will be ( if the line was dotted)

• A horizontal line
  • Will always be denoted with y is either greater than or lesser than (or greater than equal to or lesser than equal to) something
    • See the number on the graph where the line cuts y
    • Then, just consider it as y is related to that number
  • For example
    • We have a NOT DOTTED line that cuts the y axis at 5
    • Then the equation of the line is y=5
  • However now we need to consider which side will be greater to and which side will be lesser to
  • If you are finding the inequality for the shaded region
    • Then
      • The lower side of the line will be ( if the line was dotted)
      • The upper side will be
      • 
      • (
        if the line was dotted)

• If the line is like this
  • Then

• In other words, the right side of this line is (  if it is dotted)
• The left side of this line is ( if the line was dotted)
• If the Line is as follows

• Then

• In other words
  • the right side of this line is ( if the line was dotted)
  • The left side of this line is ( if it is dotted)