Solving and Graphing Inequalities

From a line to an area

• An equation such as y = 2x + 1 is satisfied by the points along one line
• Changing the equals sign to an inequality opens that line out into a whole area of the grid
• Points lying to one side of it satisfy the inequality while those on the other side fail, which is why the answer is a region rather than a line
• An inequality in one letter still describes a region on the grid
  • x ⩾ 4 covers everything on or to the right of the vertical line x = 4
  • y < 2 covers everything below the horizontal line y = 2, not including the line itself
• Two or three inequalities together describe the area where all of them hold at once, and that overlap is what a question labels R
• Solving inequalities in one letter, and showing them on a number line, is covered under linear equations and inequalities