After that, we know these characteristics of absolute value:

The absolute value of a positive number is itself: = a(a>；; 0);

The absolute value of a negative number is its reciprocal: =-a (a

The absolute value of 0 equals 0: = 0 (a = 0);

Then we can add some interesting topics here, such as: Simplify |2x-3| How to solve the problem of removing absolute numbers? When we remove the absolute number, we need to judge whether the number in the absolute number is positive or negative, which refers to the positive or negative of 2x-3, but the topic does not give the positive or negative of 2x-3, so we discuss it in categories and cover every situation. There are several possible situations:

When 2x-3

When 2x-3 >: 0, x >:

When 2x-3=0, x =；;

Do you find that the sign of 2x-3 depends on the value of x, so can it be set as the origin? If x is greater than the origin, the value of 2x-3 is greater than 0; if x is less than the origin, the value of 2x-3 is less than 0? Of course, we can also express it clearly on the number axis.

Draw this picture, this problem has been basically solved, only the final answer is left.

If x

If x>, 2x-3 >；; 0; If the absolute number is greater than zero, when the absolute number is deleted, the number in it will remain unchanged. So: | 2x-3 | = 2x-3;

If x=, then 2x-3 = 0；; The original formula is equal to 0;

It is relatively simple to get rid of an absolute number once like this, but it is not so easy to get rid of three absolute numbers at once. For example: | 2x-3 | +| 3x-5 |-5x+ 1 |

In fact, the idea of simplifying this formula is the same as that of simplifying |2x-3|, and an "origin" can be set. However, we will find that just setting an "origin" in | 2x-3 |+| 3x-5 |-5x+ 1 | seems a bit insufficient. In this case, we need to set an origin for each absolute number, and then judge the value of each single item according to this origin. Similarly, drawing a picture will express it clearly.

Step by step, if x

If x, x is on the right side of |5x+ 1| "origin" (of course, it can also be on |5x+ 1| "origin") and its absolute value is an absolute number; X is to the left of the origin of |2x-3| (or on the origin of |2x-3| if possible), and its absolute value is the reciprocal of the number in the absolute value sign; X is to the left of the "origin" of |3x-5|, and its absolute value is the reciprocal of the number in the absolute value sign. So: | 2x-3 |+| 3x-5 | 5x+1| = 2x-3+5-3x-(-5x-1) = 9-10;

if

if

In fact, there is a basic core to remove the absolute number, that is, to grasp the "origin" of each single item, then discuss the positive and negative of the absolute value of each single item, and finally remove the absolute value. This process seems complicated, but when you go deep into it, you will find it is not difficult to solve this type of problem.