How to solve the inequality x 3 2x 1 2 20

Draw |x+3|is 1 |2x-1|For 2, both are V-shaped, the first lowest point is x=-3, and the second x=1 is taken when 2.

When 1 is 2, 1 is above 2, then it is directly |x+3|-|2x-1|=2 calculates x+3-(2x-1)=2 and x+3-(-2x+1)=2

x1=2 x2=4 3 Since it is an open interval, then (4 3,2).

The solution to this problem is as follows.

When x<-3, remove the absolute value to get -(x+3)+(2x-1)<2 to get x>-6

At that time, removing the absolute value gives x+3-(2x-1)<2 gives x <

You can draw their relationships on the axes and you can solve it...

Segmented discussions. When x<-3, the original formula is equivalent to -(x+3)+(2x-1)<2 to get x<6

When -3<=x<=1 2 The original formula is equivalent to x+3+(2x-1)<2 to get x<0

When x>1 2, the original formula is equivalent to x+3-(2x-1)<2, and the solution gives x<-2, and in summary, x<0

It is discussed in 4 cases, removing the absolute value and then solving it.

1、x+3>0 2x-1>0

2、x+3<0 2x-1>0

3、x+3>0 2x-1<0

4、x+3<0 2x-1<0

Hey. When encountering this question, move the item first.

x+3|-2<|2x-1|

Let y1=|x+3|-2,y2=|2x-1|Then draw your own drawings and go. It's easy to figure out the intersection points.

You can read the answer orally by looking at the picture.

The left side of the equation can be seen as the sum of the distances from a point x to -3, -2 on the number line, and x=1, x=-6|x+3|+|x+2|=7, so between these two points is "7's.

So -6 "x "1

by ...x+2/x-3/7..;

When x 3, the equation becomes.

x+2+x-3＜7

i.e. 2x 8 i.e. x 4

So the solution of the inequality is 3 x 4

When -2 x 3; <.formula becomes.

x+2+（3-x）＜7

i.e. 5 7 constant established.

So the solution of the inequality is -2 x 3

When x -2, the formula becomes.

x-2+（3-x）＜7

i.e. -2x+1 7

That is, x -3, that is, the solution of the inequality at this time is -3 x -2, so the solution of the inequality is -3 x 4