Math 7.5 Recap

• Inequality


  A mathematical sentence that shows that two quantities are not equal
• Solution of an inequality


  The value or values that make an inequality true
• An inequality can have many solutions
• Graphing inequalities on a number line

  Use a solid circle if the value is part of the solution, use an open circle if the value is not part of the solution
• Inequality symbols


  • > is greater than
  • < is less than
  • ≥ is greater than or equal to
  • ≤ is less than or equal to
• Graphing x ≥ 8

  1. Draw a number line

  2. Plot 8 with a solid circle

  3. Shade the number line to the right of 8
• x ≤ 20

  The inequality represents that the amount James spent at the mall is less than or equal to $20
• Graphing a ≤ 4

  1. Draw a number line

  2. Plot 4 with a solid circle

  3. Shade the number line to the left of 4
• Graphing b > 3

  1. Draw a number line

  2. Plot 3 with an open circle

  3. Shade the number line to the right of 3
• If a person's height is at least 50 inches

  They can ride the rollercoaster
• If a person's height is at most 45 inches

  They can ride the helicopter ride
• If the total weight of the riders is greater than 100 pounds

  The boat will splash enough for the riders to get wet
• If the turkey's internal temperature is less than 165°F

  The turkey will be undercooked
• If the aircraft's speed is greater than 885 km/h


  It is faster than a commercial jet
• If the temperature is warmer than -6°F


  It is warmer than the previous day's temperature of -6°F
• The temperature could not have been -15°F on the next day, as it was warmer than -6°F
• The inequality -3 < p describes the graph
• Greater Than


  Inequality symbol
• Greater Than or Equal To

  Inequality symbol (the line underneath the Greater Than sign indicates also Equal To)
• Less Than


  Inequality symbol
• Less Than or Equal To

  Inequality symbol (the line underneath the Less Than sign indicates also Equal To)
• Graphing Greater Than


  • Open circle indicates that this is NOT EQUAL TO the number that is graphed
• Graphing Greater Than or Equal To

  • Closed circle indicates that this is EQUAL TO the number that is graphed
• Graphing Less Than


  • Open circle indicates that this is NOT EQUAL TO the number that is graphed
• Graphing Less Than or Equal To

  • Closed circle indicates that this is EQUAL TO the number that is graphed
• Inequality


  Comparison of numbers where one is greater than or less than another
• Inequalities use the greater than and less than symbols
• Greater than sign


  Symbol with bigger, open end facing the bigger value
• Less than sign


  Symbol with smaller, pointed end facing the smaller value
• The greater than and less than signs can be thought of as one symbol that is read differently depending on the direction it is facing
• Greater than or equal to sign

  Symbol combining greater than and equal signs
• Less than or equal to sign

  Symbol combining less than and equal signs
• Graphing inequalities on the number line

  1. Draw a point for equations

  2. Draw a line for inequalities with an open dot at the boundary value not included

  3. Fill in the boundary dot if the value is included
• Compound inequality


  Inequality with two boundary conditions, e.g. 3 < n < 7
• Using inequalities


  • Specifying a price range for a bicycle
  • Specifying a temperature range for a cat
• The best way to learn math is to practice
• The best way to learn history is to read a lot about it