Question

Solve the inequality.

|x + 5| > 12

Answer 1

DO you know what the |x+5| means?

Answer 2

|x|=x
|-x|=x

this means that for any answer that when y=x+5 is negative, meaning when y is negative, you reflect in the x axis

this makes the graph of y=|x+5|


notice that in doing this, you get two graphs, one where y=x+5
and another where y=-(x+5)

since these both cross y=12, you can do simultaneous equations to get

y=x+5
y=12
so we get 12=x+5
rearrange for x to get 12-5=x, x=7

and then

y=-(x+5)
y=12
so
12=-(x+5)
12=-x-5
x=-5-12
x=-17

so now you know that when x=7, y=12
and when x=-17, y=12



so you know that
|x+5|>12 when x is in those shaded regions so you get

x<-17
or x>7

Answer 3

\[\left| x+5 \right|\]
The x value must be in positive.

Answer 4

\[\left| x+5 \right|\] anything within those bars will be automatically made positive, even if it is negative. Whatever number you put in for as x must make the equation at least 13 or higher. So the smallest number you'll be able to put in would be 8. Hope this helped!