Inequalities

1. 4p > 8 → p > 8/4 → p > 2 This answer can also be written using the symbols (2, ∞)
   The parenthesis means that the domain of p does not include 2 { ie p can only be a number larger than 2}


2. 4r < 24 → r < 24/4 → r < 6 This can also be written using the symbols (-∞, 6)
   The parenthesis means that the domain of r does not include 6 { ie r can only be a number smaller than 6}


3. 4p ≥ 8 → p ≥ 8/4 → p ≥ 2 This can also be written using the symbols [2, ∞)
   The bracket means that the domain of p does include 2 { ie p can be equal to 2 or any number larger than 2}


4. 4r ≤ 24 → r ≤ 24/4 → r ≤ 6 This can also be written using the symbols ( -∞, 6]
   The bracket means that the domain of r does include 6 { ie r can be equal to 6 or any number smaller than 6}

The best way to check that you have the correct answer is select a value and substitute it into
the original inequality. So for the last problem let us select r = 5 and substitute it into 4r ≤ 24 → 4(5) ≤ 24 → 20≤ 24 therefore the answer is correct.

Try these problems:

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

2≤

3x + 5    2

≤8    answer

next absolute value inequalities

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