Video: Solving an Absolute Value Inequality Graphically

Bethani Gasparine

Use the graph to find the solution set of the inequality 𝑓(π‘₯)< 𝑔(π‘₯) in ℝ.

01:21

Video Transcript

Use the graph to find the solution set of the inequality 𝑓 of π‘₯ is less than 𝑔 of π‘₯ 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 π‘₯ and six being π‘₯, between zero and six where the 𝑓 of π‘₯ graph is actually less than the 𝑔 of π‘₯ graph, because notice the 𝑔 of π‘₯ graphs stays at 3.

The 𝑓 of π‘₯ graph is underneath that line here in yellow. So from zero to six, the inequality 𝑓 of π‘₯ would be less than 𝑔 of π‘₯ 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 π‘₯ graph is lower, is less than, the 𝑔 of π‘₯ graph and those values range for the π‘₯s from π‘₯ equals zero all the way up till π‘₯ equals six.

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