Absolute Value Inequalities

1. |t| > 7 Means t can equal 8, 9 and so on because they are larger than 7.    
   7 > -8 or -9 or -10 and so on.     However |-8| > 7    So can t = -8?
   Therefore what values can t be?  answer



2. |t| < 7 Means t can equal 6, 5 and so on because they are smaller than 7.    
   -8 < 7 as are -9 or -10 and so on.     However |-8| = 8 > 7    So can t = -8?
   Therefore what values can t be?  answer

If ≥ is substituted for > in |t| > 7 so it appears as this |t| ≥ 7 then t can be 7 or larger or -7 or less.
This is written t ≤ -7 or t ≥ 7     or as (-∞, -7] [7,∞)  The bracket mean that t can be 7 or -7

If ≤ is substituted for < in |t| < 7 so it appears as this |t| ≤ 7 then t can be 7 or -7 or any value between them, such as -6 etc.
This is written -7 ≤ t ≤ 7    or as [-7,7]  The bracket mean that t can be 7 or -7
Always try to solve the problem before looking at the answer.  

Try these problems and remember always try to solve the problem before looking at the answer:  

• |7t - 4| > 24   answer
  
  
• |8s + 6| < -50   answer
  
  
• |9r + 5| ≥ 59   answer
  
  
• |2b - 3| ≤ 15   answer
  
  
• |-3a + 2| ≤ 23   answer
  
  

|3x + 5|    2

≥8    answer

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