Knowing that a is any rational number, try to compare the magnitude of a and 2a.

Knowing that a is any rational number, try to compare |a|With the size of -2a: |a|<-2a。

i.e. compare |a|and the size of -2a.

When a>0, |a|=a,-2a<0.then |a|>-2aWhen a=0, |a|=0.-2a=0.then |a|>-2aWhen a=0, |a|=-a>0.-2a>0

a|-(2a)=-a+2a=a<0

then |a|<-2a

1. Add two numbers with the same sign, take the same symbol as the additive, and add the absolute value.

2. If the absolute value is equal, the sum of the two numbers of the opposite number is 0; If the absolute values are not equal, take the sign of the addition with the greater absolute value, and subtract the smaller absolute value from the larger absolute value.

3. Add two numbers that are opposite to each other to get 0.

4. Add a number to 0 and still get this number.

5. Two numbers that are opposite to each other can be added first.

6. Numbers with the same symbol can be added first.

7. Numbers with the same denominator can be added first.

8. If several numbers can be added to get an integer, they can be added first.

i.e. compare |a|and the size of -2a.

This question needs to be discussed in a categorical manner.

When a>0, |a|=a,-2a<0.then |a|>-2aWhen a=0, |a|=0.-2a=0.then |a|>-2aWhen a=0, |a|=-a>0.-2a>0

a|-(2a)=-a+2a=a<0

then |a|<-2a

|a|Always a positive number, a can be a positive number, it can also be a negative number, 1, a 0, |a|=a，-2a=-2a，|a|＞-2a，2、a＜0，|a|=-a, -2a=-2a, is positive, -2a |a|，3、a=0，-2a=|a|。

Rational numbers are a collective term for integers (positive integers, 0s, negative integers) and fractions, and are a collection of integers and fractions, i.e., the decimal part of a rational number is a finite or infinite cyclic decimal number.

Rational numbers correspond to irrational numbers (real numbers that are not rational numbers are called irrational numbers), and their decimal parts are infinite non-cyclic numbers. Rational numbers are one of the important contents in the field of "number and algebra", and they are also widely used in real life, which is the basis for continuing to learn real numbers, algebraic formulas, equations, inequalities, Cartesian coordinate systems, functions, statistics and other mathematical content and related subject knowledge.

a>0 |a|Must be greater than zero.

2a must be less than zero so |a|When >-2aa=0, both are of the same size.

a>0 |a|must be greater than zero, and -2a must also be greater than zero, so the point is to compare the magnitude of the two at a<0.

It is now known that a<0

Then the two formulas can be reduced to Compare |a| |2a|The size of the obvious in a rational number |2a| >a|Therefore a<0 -2a>|a|

To sum up: a>0 |a|When >-2aa=0, both are of the same size.

a<0 -2a>|a|

When a>0, |a|-(2a)=-a+2a=a<0, so |a|<-2a；

When a>0, |a|-(2a)=0, so |a|=-2a；

When a>0, |a|-(2a)=a+2a=3a 0, so |a|＞-2a；

a|It is always a positive number, a may be a positive number, or the nucleus will be negative.

1、a＞0,|a|=a,-2a=-2a

a|＞-2a

2, a hall brother 0, |a|=-a, -2a=-2a, are positive numbers.

2a＞|a|

3. False excavation a=0

2a=|a|

i.e. compare |a|and -2a size scale.

This topic needs to be discussed by category.

When the car is hidden a>0, |a|=a,-2a-2a

When a>0, |a|=0.-2a=0.then |a|=-2a when a0-2a>0

a|-(2a)=-a+2a=a

Rational numbers include positive and negative numbers, as well as 0

So it is discussed in three situations.

a 0 a a

a 0 a a

a 0 a a

When a is a positive number, a > a

When it is 0, a = a

When negative, a< a

i.e. compare |a|and the size of -2a.

This question needs to be discussed in a categorical manner.

When a>0, |a|=a,-2a<0.then |a|>-2aWhen a=0, |a|=0.-2a=0.

then |a|=-2aWhen a<0, the bridge trace, |a|=-a>0.-2a>0a|-(2a)=-a+2a=a<0

then |a|"Dissipation-2a