Question

Can someone explain how to do this?
|x + 3| < 5

Answer 1

x+3< 5

x+3< -5

find the value of x
look for its domain..

Answer 2

To solve for x you need to get the x by itself. So on the first equation you need to subtract 3 from each side. Which brings you to x<5-3, then solve the 5-3. So you get x<2. The second one is the same.

Answer 3

that isn't a very good explanation


there are two methods

a graphical method
to do the graphical method

draw the graph y=x+3
then draw the graph y=5
then draw the graph y=|x+3|

the |x+3| means that when it is about to cross the x axis, it will bounce off and go through positive version of negative points
for example

x+3
if i substitute x=-4
-4+3=-1
instead of -1, it will go through the point 1

so you get a graph looking like this



so you want to find where the to points intersect

you know it intersects twice

Answer 4

so looking at the graph
you know that the line y=x+3 crosses with the line y=5
so you have an equation

x+3<5
x<2


then you know that the line
y=|x+3| and y=5 cross
but |x+3| just means that any negative value, becomes positive, so instead of writing |x+3| you can see that this is x+3 but going in the opposite direction, so this is actually a reflection in the y axis so we write

-(x+3)

so this gives us another equation

-(x+3)<5
-x-3<5
-x<8
x>-8