# How do you graph the inequalities #2abs(x-4)>10# on a number line?

##### 1 Answer

There are two solutions:

The reasoning is the following:

First, you can simplify both members of the inequality by 2, obtaining

Then, we must apply the definition of the absolute value that is:

* if #z >=0 => |z| = z#.
* if

Applying this definition to our problema, we have:

*if*#(x-4) >=0 => |x-4| > 5 => x-4 > 5 => x > 9# .

if

Sorry but I don't know how to insert the graph. Anyway, it is very easy to represent it when you know the solution: you only have to draw a horizontal line, mark the point (-1) on the left side, and the point (+9) on the right side (with a regular distance between both), and then drawing thicker the portion of the line from the left extreme until the point (-1), and also drawing thicker the portion of the line from the point (+9) until the right extreme.