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

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.

To graph the inequality (2| x - 4 | > 10) on a number line, first, isolate the absolute value expression:

[ | x - 4 | > 5 ]

Then, break it into two separate inequalities:

[ x - 4 > 5 \quad \text{and} \quad x - 4 < -5 ]

Solve each inequality:

[ x > 9 \quad \text{and} \quad x < -1 ]

Now, plot these two points on the number line and shade the regions that satisfy the inequalities. This results in two intervals: one to the left of -1 and one to the right of 9, with open circles at -1 and 9 to indicate that they are not included in the solution set.