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## Homework Statement

|x+3|+|x-1| = 5

## Homework Equations

absolute value = distance from origin

distance between 2 points on a line = |x1-x2|

so |x+3| can be viewed as the distance from x to -3

and |x-1| can be viewed as the distance from x to 1

so we are trying to find a point x which has a distance from -3 and a distance from 1 that combine to equal 5...

## The Attempt at a Solution

The options that add up to equal 5 are (0+5), (5+0), (2+3), (3+2), (1+4), (4+1)

if |x+3| = 0, then x=-3.... that gives 4 instead of 5

if |x+3| = 5, then x=2 or -8.... that gives 6 and 14 instead of 5

if |x+3| = 3, then x=0 or -6... that gives 4 and 10 instead of 5

if |x+3| = 2, then x=-1 or -5... that gives 4 and 8 instead of 5

if |x+3| = 1, then x=-2 or -4... that gives 4 and 6 instead of 5

if |x+3| = 4, then x=1 or -7... that gives 4 and 12 instead of 5

^ not only is that a really inefficient way to try to solve it. but I also couldn't get the answer! :(

can someone please tell me a way to solve these problems?

edit: I just realized I neglected all the options where x is not an integer...

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