Express the graph shown in color using interval notation. Also express it as an inequality, involving x.

Solution:

This graph expressed in interval notation would be

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We know this because, the 5 is represented by a ( and infinity would be represented by ) as well. We know this starts at 5 because that is where the ( is. We know this goes on to positive infinity because the arrow leads to the positive side, and the arrow will tell us the solution goes to infinity. We will put the numbers in interval notation according to their placement on the graph, that is why 5 is on the left, and infinity is on the right.

To express this graph as an inequality, we can just look at our interval notation as well as our graph to determine that

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We know this because the ( tells us the sign will be either < or > it is greater than or less than, but not equal to. Since the arrow leads in the positive direction we know that x is greater than 5. When we express an interval in terms of inequalities we will write the answer as above because what we are saying about our inequality is the set of all real numbers x such that x is greater than 5.

Solution by Emily Johnson/Spring05