Question

How do you solve `abs(9n+8)=46`?

Answer 1

`x=(4.2,-5.88)`

Explanation:

`color(blue)(|9n+8|=46`

First of all, the equation is in absolute value

So we can make it into two equations

`color(orange)(9n+8=46`

`color(violet)(9n+8=-46`

Solve for the equations

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`rarrcolor(orange)(9n+8=46`

`rarrcolor(orange)(9n=46-8`

`rarrcolor(orange)(9n=38`

`rarrcolor(orange)(9n=38`

`rarrcolor(green)(n=38/9=4.2`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`rarrcolor(violet)(9n+8=-46`

`rarrcolor(violet)(9n=-46-8`

`rarrcolor(violet)(9n=-53`

`rarrcolor(green)(n=-53/9=-5.88`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`:.color(green)(x=(4.2,-5.88)`