Question

Solve for x and graph the solution on the number line below.

Answer 1

Please the picture attached to know the representation of the system of inequalities, whose solution set is x ≤ - 6 or x > 3.

How to graph a system of inequalities on number line

In this problem we find a system of inequalities that must be graphed on number line. The procedure is summarized below:

1. Write the system of inequalities.
2. Simplify each inequality by algebra properties.
3. Graph the resulting expressions on number line.
4. Write the solution set.

First, write the system of inequalities:

- x - 5 ≥ 1

- x - 5 < - 8

Second, simplify each inequality by algebra properties:

- x + (- 5 + 5) ≥ 1 + 5

- x + (- 5 + 5) < - 8 + 5

- x + 0 ≥ 6

- x + 0 < - 3

- x ≥ 6

- x < - 3

x ≤ - 6

x > 3

Third, graph the resulting expressions (Please see the image attached below). We plot the first inequality (x ≤ - 6) and then the second inequality (x > 3), please notice that solution set consists in two regions.

Fourth, write the solution set to the inequality:

x ≤ - 6 or x > 3