Question

Question #08cdf

Answer 1

`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`