# Video: Solving an Absolute Value Inequality Graphically

Use the graph to find the solution set of the inequality 𝑓(𝑥)< 𝑔(𝑥) in ℝ.

01:21

### Video Transcript

Use the graph to find the solution set of the inequality 𝑓 of 𝑥 is less than 𝑔 of 𝑥 in the real numbers.

The intersections of graphs are where solutions are. So here we can see these two graphs intersecting at two places.

Notice the 𝑦-values of threes stay constant. However, there’s a range, with zero being 𝑥 and six being 𝑥, between zero and six where the 𝑓 of 𝑥 graph is actually less than the 𝑔 of 𝑥 graph, because notice the 𝑔 of 𝑥 graphs stays at 3.

The 𝑓 of 𝑥 graph is underneath that line here in yellow. So from zero to six, the inequality 𝑓 of 𝑥 would be less than 𝑔 of 𝑥 in the real numbers. So we have an interval from zero to six.

And just for reclarification, here in the pink we can see where the 𝑓 of 𝑥 graph is lower, is less than, the 𝑔 of 𝑥 graph and those values range for the 𝑥s from 𝑥 equals zero all the way up till 𝑥 equals six.