# Question #08cdf

Dec 15, 2017

$x = - 1$ and $x = 4$

#### Explanation:

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

$3 + | x - 3 | = 7$
$\therefore | x - 3 | = 4$

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
$x - 3 = 4$
$\therefore x = 4 + 3$
$x = 7$

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 $- 1$.

$x - 3 = - 4$
$\therefore x = - 4 + 3$
$\implies x = - 1$

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