Question #08cdf

1 Answer
Dec 15, 2017

x= -1 and x=4

Explanation:

If we rearrange slightly we can make our operations easier to perform:

3+ |x-3| = 7
:. |x-3| = 4

We now need to consider that the expression |x-3| has both a positive and negative solution for x:

Consider the positive solution for x:
In this case we can disregard the absolute value sign
x-3=4
:. x=4+3
x=7

Consider the negative solution for x:
Now: to solve for the negative solution, we must remove the absolute value signs by multiplying both sides by -1.

x-3=-4
:. x=-4+3
=>x=-1

Thus, our solutions are x= -1 and x=4