How do you solve #abs(x-3)<4#?

1 Answer

Answer:

#-1 < x < 7#

Explanation:

Absolute value functions can be split up into two functions; represented in variable form, it would look like

#| a - b | < c#

becomes

#a - b < c# and #a - b > - c#

So, you have

#| x - 3 | < 4#

can be split up into

#x - 3 < 4# and #x - 3 > - 4#

Now we can solve each inequality to get

#x - 3 < 4# #-># add 3 to both sides

#x - cancel(3) + cancel(3) < 4 + 3#

#x<7#

and

#x - 3 > - 4# #-># add 3 to both sides to get

#x - cancel(3) + cancel(3) > -4 + 3#

#x>-1#

so your answer would be

#x > - 1#
#x < 7#

or

#-1 < x < 7#