|3| = 3 |4| = 4 |50| = 50 |-3| = 3 |57| = 57 |-1000| = 1000 |0| = 0 |-789| = 789 The last identity reads : "the absolute value of -789 is 789". The absolute value of a number is always a positive number. We can remove the bars the writing of |x|, according to the following rule : you have to distinguish two cases : if x is positive, then |x| = x, and if x is negative, then |x| = - x ( |-9| = - (-9) = 9). If there is a more complicated number between the absolute value bars, you do the same way, |2x - 4| = 2x - 4 if x > 2 (2x - 4 > 0) and |2x - 4| = -2x + 4 if x < 2 (2x - 4 < 0). How to solve |x - 5| < 3.You have to consider two cases, so you have to write down a system of equations : Hence . You can also solve this kind of equations thanks to a graph. You have to know that |x - y| < a means "the distance between x and y is smaller than a". In that case it is "the distance between x and 5 is smaller than 3". So you place the number 5 then you count 3 on both sides. As it is the sign "smaller than" and not "smaller than or equal to", 2 and 8 are not solutions of the system. |