Equations and inequalities with modules, the geometric meaning of the module

Solving equations and inequalities

By definition

For geometric content

— distance on the number line from point 0 to point

According to the General scheme

1. Find odz
2. Find zeros of all functions pdmadly
3. Note the zeros on DHS and split DHS into the gaps
4. To find a solution in each of the intervals (and check whether this razvyazok in the considered period).

The use of geometric meaning of the module (a>0)

1. or
2. or
3. or
4. 
5. 
6. or
7. 

The use of special ratios

Example of solution of inequalities with module

Rozwarte inequality:

Solutions:

Offer to square the left and right part of the inequality:

Answer:

Example of solution of inequalities with multiple modules

Rozwarte inequality:

Solutions:

1) odz; 2) the Zeros odnodolnyh functions;

So