Inequalities

• What is the definition of inequalities?

  Inequalities show relationships between unequal expressions
• What are the symbols used for inequalities?

  <, >, ≤, ≥, ≠
• What does the symbol $≤$ represent?


  Less than or equal to
• What does the symbol $≠$ represent?


  Not equal to
• How are inequalities represented on a number line?

  Using open and closed circles
• What does an open circle represent on a number line?

  Numbers greater or less than
• What does a closed circle represent on a number line?

  Numbers greater or less than or equal to
• How would you represent the inequality $x ≤ 0$ on a number line?


  Closed circle at 0, arrow left
• How would you represent the inequality $x < 2$ on a number line?


  Open circle at 2, arrow left
• How would you represent the inequality $x ≥ 0$ on a number line?


  Closed circle at 0, arrow right
• What is the first step to solve the inequality $3m +$$2 > -4$?


  Subtract 2 from both sides
• What is the next step after simplifying $3m > -6$?


  Divide both sides by 3
• What is the solution to the inequality $3m > -6$?


  $m > -2$
• What is the first step to solve the inequality $3(3 - x) < 6$?


  Expand the brackets
• What do you get after expanding $3(3 - x) < 6$?


  $9 - 3x < 6$
• What is the next step after $9 - 3x < 6$?


  Subtract 9 from both sides
• What is the result after subtracting 9 from $9 - 3x < 6$?


  $-3x < -3$
• What is the final step to solve $-3x < -3$?


  Divide by -3 and reverse inequality
• What is the solution to the inequality $-3x < -3$?


  $x > 1$
• What are integer solutions to inequalities?

  • Infinite solutions exist
  • Any number greater than a specific value is possible
  • Example: Numbers greater than 3
• What are integer subsets in inequalities?

  • Integer subsets are possible numbers
  • Example: Integers between 16 and 51
  • Include all integers greater than a specific value
• What is an example of an integer subset in inequalities?

  Integers between 16 and 51
• What does it mean if an inequality has infinite solutions?

  Any number greater than a specific value is possible