Positives & Negatives

Things one must know:

• Absolute value: how far a number is from zero on a number line.
• Double negative = positive.
• When multiplying or dividing two numbers: if the signs are the same, the answer is positive, if not, the answer is negative. 
• When multiplying or dividing a group of nonzero numbers, the result will be positive if there's an even number of negative numbers, and the result will be negative if there's an odd number of negative numbers.
• Use a table to test positive or negative numbers systematically.
• The absolute value | x - y | can be interpreted as the distance between x  and y. Ie. | x - 3 | < 4 can be rephrased as "the distance between x and 3 is less than 4 units", this means -1 < x < 7. Find the midpoint or the average to set up the inequality.
• Whenever you see inequalities with zero on either side of the inequality, you should consider testing positive/negative case
  
  Complex absolute value equations
  
• Two different variables and no constants in absolute value expressions, it is usually easiest to test positive/negative numbers
• One variable and one or more constants, it is usually easier to solve with an algebraic approach. You need to consider two real cases:
  1) neither expression changes sign
  2) one expression changes sign
  Check the validity of the solutions!