Cumulative Standards Review
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Looking at the given graph, we can conclude that the values that are solutions to the inequality are outside the interval. In this case, the graph can be represented by an absolute value inequality as |A|> b.
A
Looking at the given graph, we can conclude that the values that are solutions to the inequality are outside the interval from 1 to 3. Because the endpoints are represented by open points, they are not included in the solution set.
In this case, the graph can be represented by an absolute value inequality as |A|> b. Absolute values can be interpreted as the distance away from a midpoint. For one-variable absolute value inequalities, this distance can be represented by the endpoints and the midpoint on a number line.
Because our inequality needs a distance from a midpoint, we should find the halfway point between the endpoints. We can do this by calculating their mean. Mean=1+ 3/2= 2 Now we need to find the distance between this midpoint and each of the endpoints. To do this, we will find the difference between each of the endpoints and the midpoint. Distance= 2- 1= 3- 2= 1
To write the absolute value inequality, we can show that the difference between a number x and the midpoint is greater than the distance we found above. |x- Midpoint| > Distance |x- 2| > 1 If we subtract 3 from both sides of the inequality, we see that the absolute value inequality in option A is equivalent to the one we found above. |x-2|-3 > -2