if (p+7) is positive, this becomes (p+7) > 2
solve for p to get p > -5
if (p+7) is negative, this becomes (p+7) < -2
solve for p to get p < -9
your solution is p > -5 or p < -9
p has to be greater than -5 or smaller than -9
let's see what happens if these guidelines are violated.
if p = -7, you get abs(-7+7) > 2 which becomes 0 > 2 which is false.
this is as it should be because -7 is not greater than -5 and not smaller than -9.
now let's see what happens if these guidelines are not violated.
if p = 0, that's greater than -5 and you get abs(0+7) > 2 which becomes 7 > 2 which is true.
if p = -20, that's smaller than -9 and you get abs(-20+7) > 2 which becomes abs(-13) > 2 which becomes 13 > 2 which is true.
looks like we have the solution.
to confirm, we can graph the equation of abs(x+7) and the equation of y = 2 to see what regions of the graph u = abs(x+7) is greater than y = 2.
that graph is shown below:
look below the graph for further comments.
you can see from the graph that when x < -9 and x > -5, the graph of y = abs(x+7) has a value that is greater than the graph of y = 2.
