# How to graph and solve systems of linear inequalities, using the double-number line?

##### 1 Answer

Solving system of linear inequalities.

Using a double number-line to solve a system of 2 linear inequalities. (Math article written by Nghi Nguyen)

#### Explanation:

**Example 1** . Solve the system:

2x - 3 < 11 (1)

3x > x + 6 (2)

First, solve the 2 inequalities:

Solve (1) --> 2x < 14 -->

On a number-line, draw the solution set:

+++++++++++++0 +++++3++++++++++7------------------

Solve (2) --> 3x - x > 6 --> 2x > 6 -->

Draw the solution set on the second number-line:

----------------------0---------3++++++++++7+++++++++++

By superimposing, we see that the combined solution set of the system is the open interval (3, 7). The 2 end points are not included.

**Example 2** . Solve the system:

3x + 7 < x - 1 (1)

2x - 4 > - x + 5 (2)

Solve (1) --> 2x < - 8 -->

Solve (2) --> 3x > 9 -->

+++++++++++ -4--------------- 0 -------------3----------------------

------------------ -4 -------------------------------3++++++++++++++

By superimposing, we see that the combined solution set are the

open intervals: (-inf. -4) and (3, +inf.)

NOTE. This method can be used to solve a system of 3 linear inequalities.