Express linear inequalities graphically and algebraically

Lessons

• Introduction
  i) What is an inequality?
  ii) How to solve linear inequalities?
  iii) How to graph inequalities on a number line?

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• 1.
  Express the following inequalities algebraically.
  a)

  
  
  
  
  
  b)

  
  
  
  
  
  c)

  
  
  
  
  

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• 2.
  Graph each inequality on a number line.
  a)

  $3.6$ > $x$
  
  
  b)

  $x \le - 3\frac{4}{7}$
  
  
  c)

  $y \le 11$
  
  
  d)

  $5$ < $- \frac{1}{6}$x
  
  

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• 3.
  Find the possible values of $x$ on a number line.
  a)

  $x \ge 6$ and $x \le 11$
  
  
  b)

  $x$ > $2\frac{3}{7}$ and $x \le 5$
  
  
  c)

  $x \ge - 3.6$ and $x \le 0.25$
  
  
  d)

  $x$ > $-7$ and $x \le - 3\frac{1}{2}$
  
  

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• 4.
  A Christmas tree must be 2 feet or taller so that the farmers will cut it down and sell it in the market.
  a)

  Use a number line to express the situation.
  
  
  b)

  Express the situation in a statement.
  
  

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