how to solve this ? |x+1|-|x+2|<=2

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lfryerda | High School Teacher | (Level 2) Educator

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In order to find the solution to the inequality, we need to find the intersection points of the related equation 


and then determine for each region between those intersection points, which region satisfies the inequality.

There are two cases to consider when solving the inequality.

Case 1:


`-1=2`   there are no intersections from this case since this is not a valid equation.

Case 2:




For the region to the left of the point `x=-1/2` , we see that by using a test point such as `x=-1` and substituting it into the inequality, we get:




which means that the region `x in (-infty, -1/2]` is a solution to the inequality.

From the region to the right of the point `x=-1/2` , by using a test point such as `x=1` , we get:




which means the region `x in [-1/2,infty)` is also a solution to the inequality

This means that all real numbers `x in R` are a solution to the inequality.

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